{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/4.jpg' \/><\/center> <br\/> T\u00ecm m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean bi\u1ebft t\u00edch c\u1ee7a \u01b0\u1edbc s\u1ed1 l\u1edbn nh\u1ea5t v\u1edbi b\u1ed9i s\u1ed1 nh\u1ecf nh\u1ea5t kh\u00e1c 0 c\u1ee7a n\u00f3 l\u00e0 625 <br\/>S\u1ed1 \u0111\u00f3 l\u00e0: _input_ ","hint":"\u01af\u1edbc s\u1ed1 l\u1edbn nh\u1ea5t l\u00e0 ch\u00ednh n\u00f3, b\u1ed9i nh\u1ecf nh\u1ea5t kh\u00e1c 0 l\u00e0 ch\u00ednh n\u00f3","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u01af\u1edbc s\u1ed1 l\u1edbn nh\u1ea5t c\u1ee7a a l\u00e0 a B\u1ed9i nh\u1ecf nh\u1ea5t kh\u00e1c 0 c\u1ee7a a c\u0169ng l\u00e0 a Khi \u0111\u00f3 t\u00edch l\u00e0: a . a = 625 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a <br\/> \u01af\u1edbc s\u1ed1 l\u1edbn nh\u1ea5t c\u1ee7a a l\u00e0 a <br\/> B\u1ed9i s\u1ed1 nh\u1ecf nh\u1ea5t kh\u00e1c 0 c\u1ee7a a l\u00e0 a <br\/> T\u00edch c\u1ee7a \u01b0\u1edbc s\u1ed1 l\u1edbn nh\u1ea5t v\u1edbi b\u1ed9i s\u1ed1 nh\u1ecf nh\u1ea5t l\u00e0: <br\/> a . a = 625 = $5^4 = (45^2)^2 = 25^2$ $\\Rightarrow$ a = 25 <br\/> <span class='basic_pink'> S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 25 <\/span> "}]}],"id_ques":791},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["34"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/13.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean n sao cho n + 1 l\u00e0 \u01b0\u1edbc c\u1ee7a 105; n - 1 l\u00e0 b\u1ed9i c\u1ee7a 11. <br\/> S\u1ed1 \u0111\u00f3 l\u00e0: n = _input_ ","hint":"T\u00ecm t\u1eadp \u01af(105) r\u1ed3i t\u00ecm t\u1eadp c\u00e1c gi\u00e1 tr\u1ecb n, th\u1eed t\u1eebng gi\u00e1 tr\u1ecb c\u1ee7a n n\u1ebfu n - 1 t\u01b0\u01a1ng \u1ee9ng l\u00e0 b\u1ed9i c\u1ee7a 11 th\u00ec \u0111\u00f3 l\u00e0 s\u1ed1 c\u1ea7n t\u00ecm","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ecm t\u1eadp \u01af(105) <br\/> V\u00ec $(n + 1) \\in \u01af(105)$ n\u00ean ta t\u00ecm \u0111\u01b0\u1ee3c t\u1eadp c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n <br\/> <b> B\u01b0\u1edbc 2 : <\/b> Th\u1eed l\u1ea7n l\u01b0\u1ee3t c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n \u0111\u1ec3 t\u00ecm n - 1 th\u1ecfa m\u00e3n l\u00e0 b\u1ed9i c\u1ee7a 11 <br\/> N\u1ebfu n - 1 $\\in B(11)$ th\u00ec gi\u00e1 tr\u1ecb \u0111\u00f3 c\u1ee7a n l\u00e0 s\u1ed1 c\u1ea7n t\u00ecm<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>V\u00ec (n + 1) $\\in$ \u01af(105) n\u00ean ta c\u00f3: <br\/> (n + 1) $\\in$ \u01af(105) = {1; 3; 5; 7; 15; 21; 35; 105} <br\/> $\\Rightarrow$ n $\\in$ {0; 2; 4; 6; 14; 20; 34; 104} <br\/> V\u00ec n - 1 l\u00e0 b\u1ed9i c\u1ee7a 11 n\u00ean ta x\u00e9t t\u1eebng gi\u00e1 tr\u1ecb c\u1ee7a n <br\/> V\u1edbi n = 2 $\\Rightarrow $ n - 1 = 1 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1edbi n = 4 $\\Rightarrow$ n - 1 = 3 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1edbi n = 6 $\\Rightarrow$ n - 1 = 5 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1edbi n = 14 $\\Rightarrow$ n - 1 = 13 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1edbi n = 20 $\\Rightarrow$ n - 1 = 19 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1edbi n = 34 $\\Rightarrow$ n - 1 = 33 $\\vdots$ 11 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> V\u1edbi n = 104 $\\Rightarrow$ n - 1 = 103 $\\not \\vdots$ 11 (lo\u1ea1i) <br\/> V\u1eady ch\u1ec9 c\u00f3 n = 34 l\u00e0 th\u1ecfa m\u00e3n n + 1 l\u00e0 \u01b0\u1edbc c\u1ee7a 105 v\u00e0 n - 1 l\u00e0 b\u1ed9i c\u1ee7a 11 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 34 <\/span> "}]}],"id_ques":792},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["841"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/12.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean n l\u1edbn nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 sao cho n chia 17 d\u01b0 8, chia 25 d\u01b0 16 <br\/> S\u1ed1 \u0111\u00f3 l\u00e0: n = _input_ ","hint":"Ta \u0111i t\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean n l\u1edbn nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 sao cho (n - 8) $\\vdots$ 17 v\u00e0 (n - 16) $\\vdots$ 25","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b>V\u00ec n chia 17 d\u01b0 8, chia 25 d\u01b0 16 n\u00ean: <br\/> (n - 8) $\\vdots$ 17 v\u00e0 (n - 16) $\\vdots$ 25 (n > 25) <br\/> <b> B\u01b0\u1edbc 2 : <\/b> Bi\u1ebfn \u0111\u1ed5i t\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean m sao cho (n + m) $\\vdots$ 17 v\u00e0 (n + m) $\\vdots$ 25 <br\/> Khi \u0111\u00f3 (n + m) $\\vdots$ BCNN(17; 25) <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n <br\/> Ch\u1ecdn gi\u00e1 tr\u1ecb c\u1ee7a n th\u1ecfa m\u00e3n n l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec n chia 17 d\u01b0 8 n\u00ean (n - 8) $\\vdots$ 17 (n > 8) <br\/> $\\Rightarrow$ n = 17a + 8 ($a \\in \\mathbb{N}$) <br\/> $\\Rightarrow$ n + 9 $\\vdots$ 17 (1)<br\/> V\u00ec n chia 25 d\u01b0 16 n\u00ean (n - 16) $\\vdots$ 25 (n > 16) $\\Rightarrow$ n = 25b + 16 ($b \\in \\mathbb{N}$) <br\/> $\\Rightarrow$ (n + 9) $\\vdots$ 25 (2) <br\/> <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ n + 9 $\\vdots$ BCNN(17; 25) <br\/> $\\Rightarrow$ (n + 9) $\\vdots$ 425 <br\/> $\\Rightarrow$ n = 425k - 9 ($k \\in \\mathbb{N}^*$) <br\/> V\u1edbi k = 1 $\\Rightarrow$ n = 425 . 1 - 9 = 416 <br\/> V\u1edbi k = 2 $\\Rightarrow$ n = 425 . 2 - 9 = 841 <br\/> V\u1edbi k = 3 $\\Rightarrow$ n = 425 . 3 - 9 = 1266 (lo\u1ea1i) <br\/> V\u00ec n l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t c\u00f3 3 ch\u1eef s\u1ed1 n\u00ean n = 841<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 841 <\/span> "}]}],"id_ques":793},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["11"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/7.jpg' \/><\/center> <br\/> M\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean chia 3 d\u01b0 2, chia 5 d\u01b0 1. V\u1eady s\u1ed1 \u0111\u00f3 chia 15 \u0111\u01b0\u1ee3c d\u01b0 l\u00e0: _input_ ","hint":"G\u1ecdi s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 n, bi\u1ebfn \u0111\u1ed5i n v\u1ec1 d\u1ea1ng n = 15k + r, khi \u0111\u00f3 r l\u00e0 s\u1ed1 d\u01b0 c\u1ee7a ph\u00e9p chia n cho 15","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> G\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u00f3 l\u00e0 n. <br\/> V\u00ec n chia 3 d\u01b0 2, chia 5 d\u01b0 1 n\u00ean: n = 3a + 2; n = 5b + 1 <br\/> <b> B\u01b0\u1edbc 2 : <\/b> Bi\u1ebfn \u0111\u1ed5i t\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean m sao cho (n + m) $\\vdots$ 3 v\u00e0 (n + m) $\\vdots$ 5 <br\/> Khi \u0111\u00f3 (n + m) $\\in$ BC(3; 5) <br\/> <b> B\u01b0\u1edbc 3: <\/b> Bi\u1ebfn \u0111\u1ed5i n v\u1ec1 d\u1ea1ng n = 15k + r ($k \\in \\mathbb{N}$), r ch\u00ednh l\u00e0 s\u1ed1 d\u01b0 khi chia n cho 15 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u00f3 l\u00e0 n <br\/> V\u00ec n chia 3 d\u01b0 2 n\u00ean (n - 2) $\\vdots$ 3 $\\Rightarrow$ n = 3a + 2 ($a \\in \\mathbb{N}$) <br\/> n chia 5 d\u01b0 1 n\u00ean (n - 1) $\\vdots$ 5 $\\Rightarrow$ n = 5b + 1 ($b \\in \\mathbb{N}$) <br\/> n = 3a + 2 $\\Rightarrow$ n + 4 = 3a + 2 + 4 = 3a + 6 $\\vdots$ 3 (1) <br\/> M\u1eb7t kh\u00e1c: n = 5b + 1 $\\Rightarrow$ n + 4 = 5b + 1 + 4 = 5b + 5 $\\vdots$ 5 (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ n + 4 $\\in$ BC(3; 5) = {0; 15; 30; 45;...} = B(15) <br\/> V\u00ec n + 4 = B(15) n\u00ean n + 4 = 15k ($k \\in \\mathbb{N}$) <br\/> $\\begin{align*} \\Rightarrow n & = 15k - 4 (k \\in \\mathbb{N}) \\\\ & = 15(k - 1) + 15 - 4 \\\\ &=15(k - 1) + 11 \\end{align*}$ <br\/> V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean n khi chia cho 15 \u0111\u01b0\u1ee3c d\u01b0 l\u00e0 11 <br\/> <span class='basic_pink'> S\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 11 <\/span> "}]}],"id_ques":794},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["420"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"Ba con t\u00e0u c\u1eadp b\u1ebfn theo l\u1ecbch nh\u01b0 sau: T\u00e0u I c\u1ee9 15 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn, t\u00e0u II c\u1ee9 20 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn, t\u00e0u III c\u1ee9 12 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn. L\u1ea7n \u0111\u1ea7u c\u1ea3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o ng\u00e0y th\u1ee9 6. H\u1ecfi sau \u0111\u00f3 \u00edt nh\u1ea5t bao l\u00e2u 3 t\u00e0u l\u1ea1i c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6<br\/> \u0110\u00e1p s\u1ed1: _input_ ng\u00e0y","hint":"Th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6 l\u00e0 BCNN(15; 20; 12; 7)","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi th\u1eddi \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn l\u00e0 x <br\/> L\u1ea7n \u0111\u1ea7u 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn l\u00e0 th\u1ee9 6, sau 7 ng\u00e0y th\u00ec l\u1ea1i \u0111\u1ebfn th\u1ee9 6 <br\/> N\u00ean \u0111\u1ec3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6 th\u00ec x $\\vdots$ 7 <br\/> Th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6 l\u00e0 x = BCNN(15; 20; 12) <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi x l\u00e0 th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn (x > 20) <br\/> V\u00ec t\u00e0u I c\u1ee9 15 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn, t\u00e0u II c\u1ee9 20 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn, t\u00e0u III c\u01b0 12 ng\u00e0y th\u00ec c\u1eadp b\u1ebfn <br\/> $\\Rightarrow$ x = BCNN(15; 20; 12) <br\/> L\u1ea7n \u0111\u1ea7u 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6, sau 7 ng\u00e0y th\u00ec l\u1ea1i \u0111\u1ebfn th\u1ee9 6 <br\/> N\u00ean \u0111\u1ec3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6 th\u00ec x $\\vdots$ 7 <br\/> V\u1eady th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 3 t\u00e0u c\u00f9ng c\u1eadp b\u1ebfn v\u00e0o th\u1ee9 6 l\u00e0: <br\/> x = BCNN(15; 20; 12; 7) = 420 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 420 <\/span> "}]}],"id_ques":795},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"Ba \u00f4 t\u00f4 c\u00f9ng kh\u1edfi h\u00e0nh m\u1ed9t l\u00fac t\u1eeb m\u1ed9t b\u1ebfn. Th\u1eddi gian c\u1ea3 \u0111i l\u1eabn v\u1ec1 c\u1ee7a xe th\u1ee9 nh\u1ea5t l\u00e0 40 ph\u00fat, xe th\u1ee9 2 l\u00e0 50 ph\u00fat, xe th\u1ee9 3 l\u00e0 30 ph\u00fat. Khi tr\u1edf v\u1ec1 b\u1ebfn m\u1ed7i xe ngh\u1ec9 10 ph\u00fat r\u1ed3i ti\u1ebfp t\u1ee5c ch\u1ea1y. H\u1ecfi sau \u00edt nh\u1ea5t bao l\u00e2u c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn.<br\/> \u0110\u00e1p s\u1ed1: _input_ gi\u1edd","hint":"Th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn l\u00e0 BCNN(40; 50; 60)","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi th\u1eddi \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn l\u00e0 x (ph\u00fat) <br\/> Th\u1eddi gian xe c\u1ea3 \u0111i, v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe I l\u00e0: 50 ph\u00fat <br\/> Th\u1eddi gian c\u1ea3 \u0111i, v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe II l\u00e0: 60 ph\u00fat <br\/> Th\u1eddi gian c\u1ea3 \u0111i, v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe III l\u00e0: 40 ph\u00fat <br\/> Th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn: x = BCNN(50; 60; 40) <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn l\u00e0 x (ph\u00fat) <br\/> V\u00ec m\u1ed7i xe \u0111i v\u1ec1 \u0111\u1ec1u ngh\u1ec9 10 ph\u00fat r\u1ed3i m\u1edbi ch\u1ea1y ti\u1ebfp n\u00ean: <br\/> Th\u1eddi gian c\u1ea3 \u0111i, v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe I l\u00e0: <br\/> 40 + 10 = 50 (ph\u00fat) <br\/> Th\u1eddi gian c\u1ea3 \u0111i, v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe II l\u00e0: <br\/> 50 + 10 = 60 (ph\u00fat) <br\/> Th\u1eddi gian c\u1ea3 \u0111i v\u1ec1 v\u00e0 ngh\u1ec9 c\u1ee7a xe III l\u00e0: <br\/> 30 + 10 = 40 (ph\u00fat) <br\/> N\u00ean th\u1eddi gian \u00edt nh\u1ea5t \u0111\u1ec3 c\u1ea3 3 xe c\u00f9ng r\u1eddi b\u1ebfn l\u00e0: <br\/> x = BCNN(50; 60; 40) = 600 (ph\u00fat) <br\/> \u0110\u1ed5i 600 ph\u00fat = 10 gi\u1edd <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 10 <\/span> "}]}],"id_ques":796},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["36"],["24"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/7.jpg' \/><\/center> <br\/> Bi\u1ebft $BCNN(a, b) . \u01afCLN(a, b) = a . b$ <br\/> T\u1ed5ng hai s\u1ed1 b\u1eb1ng 60, t\u1ed5ng gi\u1eefa \u01afCLN v\u00e0 BCNN l\u00e0 84. T\u00ecm hai s\u1ed1 \u0111\u00f3. <br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_; _input_ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> T\u00ecm \u01afCLN(a, b) = ? d\u1ef1a v\u00e0o \u0111i\u1ec1u ki\u1ec7n b\u00e0i cho a + b = 60 v\u00e0 \u01afCLN(a, b) + BCNN(a, b) = 84 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Th\u1eed l\u1ea7n l\u01b0\u1ee3t t\u1eebng gi\u00e1 tr\u1ecb c\u1ee7a d \u0111\u1ec3 t\u00ecm a, b th\u1ecfa m\u00e3n y\u00eau c\u1ea7u c\u1ee7a b\u00e0i to\u00e1n <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi hai s\u1ed1 c\u00e0n t\u00ecm l\u00e0 a v\u00e0 b ($a, b \\in \\mathbb{N}$) <br\/> V\u00ec t\u1ed5ng hai s\u1ed1 l\u00e0 60 n\u00ean: a + b = 60 <br\/> G\u1ecdi \u01afCLN(a, b) = d ($d \\in \\mathbb{N}$) <br\/> $\\begin{cases}a = a_{1}d \\\\ b = b_{1}d \\end{cases} (a_{1}, b_{1}) = 1$ <br\/> BCNN(a, b) = $a_{1} . b_{1} . d$ <br\/> $\\Rightarrow$ \u01afCLN(a, b) + BCNN(a, b) = $d + a_{1}.b_{1}.d = d(1 + a_{1}.b_{1}) = 84$ (1) <br\/> $a + b = a_{1}d + b_{1}d = (a_{1} + b_{1})d = 60$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ d $\\in$ \u01afC(84; 60) = {1; 2; 3; 4; 6; 12} <br\/> V\u1edbi d = 1 $\\Rightarrow$ $\\begin{cases}a = a_{1} + b_{1} = 60 \\\\ a_{1}.b_{1} = 83 \\text{(lo\u1ea1i)} \\end{cases}$ <br\/> V\u1edbi d = 2 $\\begin{cases}a = a_{1} + b_{1} = 30 \\\\ a_{1}.b_{1} = 23 \\text{(lo\u1ea1i)} \\end{cases}$ <br\/> V\u1edbi d = 3 $\\begin{cases}a = a_{1} + b_{1} = 20 \\\\ a_{1}.b_{1} = 27 = 3 . 9 = 1 . 27 \\text{(lo\u1ea1i)} \\end{cases}$ <br\/> V\u1edbi d = 4 $\\begin{cases}a = a_{1} + b_{1} = 15 \\\\ a_{1}.b_{1} = 20 = 4 . 5 = 2 . 10 = 1 . 20 \\text{(lo\u1ea1i)} \\end{cases} $ <br\/> V\u1edbi d = 6 $\\begin{cases}a = a_{1} + b_{1} = 10 \\\\ a_{1}.b_{1} = 13 \\text{(lo\u1ea1i)} \\end{cases}$ <br\/> V\u1edbi d = 12 $\\begin{cases}a = a_{1} + b_{1} = 5 \\\\ a_{1}.b_{1} = 6 = 2 . 3 = 1 . 6 \\end{cases}$ $ \\Rightarrow \\begin{cases}a_{1} = 2 \\\\ b_{1} = 3 \\end{cases} \\Rightarrow \\begin{cases}a = a_{1}.d = 2 . 12 = 24 \\\\b = b_{1} . d = 3 . 12 = 36 \\end{cases} $ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 24; 36 <\/span> "}]}],"id_ques":797},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["15"],["18"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean a, b (10 < a < b). Bi\u1ebft \u01afCLN(a, b) = 3 v\u00e0 BCNN(a, b) = 90 <br\/> Hai s\u1ed1 \u0111\u00f3 l\u00e0: a = _input_ ; b = _input_","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> V\u00ec \u01afCLN(a, b) = 3 $\\Rightarrow$ $\u01afCLN \\left( \\dfrac{a}{3}, \\dfrac{b}{3}\\right) = 1$ <br\/> T\u00ecm t\u00edch a.b theo c\u00f4ng th\u1ee9c a . b = \u01afCLN(a, b) . BCNN(a, b) <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh t\u00edch $\\dfrac{a}{3}. \\dfrac{b}{3}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Vi\u1ebft t\u00edch c\u1ee7a $\\dfrac{a}{3}. \\dfrac{b}{3}$ d\u01b0\u1edbi d\u1ea1ng t\u00edch hai s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau <br\/> X\u00e9t t\u1eebng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ec3 t\u00ecm a v\u00e0 b <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec \u01afCLN(a, b) = 3 $\\Rightarrow$ $\u01afCLN \\left( \\dfrac{a}{3}, \\dfrac{b}{3}\\right) = 1$ <br\/> Ta c\u00f3: a . b = \u01afCLN(a, b) . BCNN(a, b) = 3 . 90 = 270 <br\/> $\\Rightarrow$ $\\dfrac{a}{3}. \\dfrac{b}{3} = \\dfrac{270}{3 . 3} = 30$ <br\/> V\u00ec $\\left(\\dfrac{a}{3}, \\dfrac{b}{3}\\right) = 1$ n\u00ean ta vi\u1ebft 30 th\u00e0nh t\u00edch hai th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau <br\/> 30 = 1 . 30 = 5 . 6 = 2 . 15 = 3 . 10 ta c\u00f3: <br\/>TH1: $\\begin{cases} \\dfrac{a}{3} = 5\\\\ \\dfrac{b}{3} = 6 \\end{cases} \\Rightarrow \\begin{cases} a = 15 \\\\ b = 18\\end{cases}$ <br\/> TH2: $\\begin{cases} \\dfrac{a}{3} = 1\\\\ \\dfrac{b}{3} = 30 \\end{cases} \\Rightarrow \\begin{cases} a = 3 \\\\ b = 90 \\end{cases}$ (lo\u1ea1i) <br\/> TH3: $\\begin{cases} \\dfrac{a}{3} = 2\\\\ \\dfrac{b}{3} = 15 \\end{cases} \\Rightarrow \\begin{cases} a = 6 \\\\ b = 45 \\end{cases}$ (lo\u1ea1i) <br\/> TH4: $\\begin{cases} \\dfrac{a}{3} = 3\\\\ \\dfrac{b}{3} = 10 \\end{cases} \\Rightarrow \\begin{cases} a = 9 \\\\ b = 30 \\end{cases}$ (lo\u1ea1i) <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 15; 18 <\/span> <br\/> <span class='basic_left'><span class='basic_green'> <i>Nh\u1eadn x\u00e9t: V\u1edbi d\u1ea1ng b\u00e0i cho bi\u1ebft \u01afCLN(a, b) = d; BCNN(a, b) = m t\u00ecm a, b ta l\u00e0m nh\u01b0 sau: <br\/> B\u01b0\u1edbc 1: T\u00ecm t\u00edch a.b theo c\u00f4ng th\u1ee9c a . b = \u01afCLN(a, b) . BCNN(a, b) <br\/> <b> B\u01b0\u1edbc 2: T\u00ednh t\u00edch $\\dfrac{a}{d}. \\dfrac{b}{d}$ <br\/> B\u01b0\u1edbc 3: Vi\u1ebft t\u00edch tr\u00ean th\u00e0nh t\u00edch hai th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau sau \u0111\u00f3 x\u00e9t t\u1eebng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ec3 t\u00ecm a v\u00e0 b <\/span> "}]}],"id_ques":798},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["36"],["30"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","ques":"T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean a, b. Bi\u1ebft a - b = 6, BCNN(a, b) = 180 <br\/> Hai s\u1ed1 \u0111\u00f3 l\u00e0: a = _input_; b = _input_","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi \u01afCLN(a, b) = d ta \u0111i t\u00ecm d $\\in$ \u01afC(a - b, BCNN(a, b)) <br\/> Thay d v\u00e0o c\u00f4ng th\u1ee9c a . b = \u01afCLN(a, b) . BCNN(a, b) k\u1ebft h\u1ee3p \u0111i\u1ec1u ki\u1ec7n a - b = 6 \u0111\u1ec3 t\u00ecm a, b<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi \u01afCLN(a, b) = d khi \u0111\u00f3: a = dm, b = dn; (m, n) = 1 <br\/> a - b = dm - dn = d(m - n) $\\Rightarrow$ d $\\in$ \u01af(a - b) hay d $\\in$ \u01af(6) <br\/> V\u00ec BCNN(a, b) = 180 $\\Rightarrow$ d $\\in$ \u01af(180) <br\/> $\\Rightarrow$ d $\\in$ \u01afC(6; 180) m\u00e0 \u01afCLN(6; 180) = 6 $\\Rightarrow$ d $\\in$ \u01af(6) = {1; 2; 3; 6} <br\/> V\u1edbi d = 1 $\\Rightarrow$ a . b = 1 . 180 = 180, a - b = 6 (kh\u00f4ng t\u1ed3n t\u1ea1i a, b th\u1ecfa m\u00e3n) <br\/> V\u1edbi d = 2 $\\Rightarrow$ a . b = 2 . 180 = 360, a - b = 6 (kh\u00f4ng t\u1ed3n t\u1ea1i a, b th\u1ecfa m\u00e3n) <br\/> V\u1edbi d = 3 $\\Rightarrow$ a . b = 3 . 180 = 540, a - b = 6 (kh\u00f4ng t\u1ed3n t\u1ea1i a, b th\u1ecfa m\u00e3n) <br\/> V\u1edbi d = 6 $\\Rightarrow$ a . b = 6 . 180 = 1080, a - b = 6 $\\Rightarrow$ a = 36; b = 30 <b>(th\u1ecfa m\u00e3n) <\/b><br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 36; 30 <\/span> "}]}],"id_ques":799},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["34650"]]],"list":[{"point":10,"width":80,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai16/lv3/img\/11.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean x nh\u1ecf nh\u1ea5t bi\u1ebft x $\\vdots$ 35; x $\\vdots$ 150 v\u00e0 x $\\vdots$ 99 <br\/> V\u1eady x = _input_","hint":"x = BCNN(35; 150; 99)","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> GV\u00ec x l\u00e0 s\u1ed1 nh\u1ecf nh\u1ea5t, x $\\vdots$ 35; x $\\vdots$ 150 v\u00e0 x $\\vdots$ 99 <br\/> N\u00ean x = BCNN(35; 150; 99) b\u00e0i to\u00e1n quy v\u1ec1 b\u00e0i to\u00e1n t\u00ecm BCNN<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec x $\\vdots$ 35 $\\Rightarrow$ x $\\in$ B(35) (1) <br\/> V\u00ec x $\\vdots$ 150 $\\Rightarrow$ x $\\in$ B(150) (2) <br\/> V\u00ec x $\\vdots$ 99 $\\Rightarrow$ x $\\in$ B(99) (3)<br\/> T\u1eeb (1), (2), (3) v\u00e0 v\u00ec x nh\u1ecf nh\u1ea5t $\\Rightarrow$ x = BCNN(35; 150; 99) <br\/> Ta c\u00f3: $35 = 5 . 7$ ; $150 = 2 . 3 . 5^2$ ; $99 = 3^2 . 11$ <br\/> $\\Rightarrow$ x = BCNN(35; 150; 99) = $2 . 3^2 . 5^2 . 7 . 11 = 34650$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 34650 <\/span> "}]}],"id_ques":800}],"lesson":{"save":0,"level":3}}