{"common":{"save":0,"post_id":"8076","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8877","post_id":"8076","mon_id":"1159278","chapter_id":"1159330","question":"<p>Kh\u1ed1i 9 m\u1ed9t tr\u01b0\u1eddng THCS có s\u1ed1 l\u1edbp nhi\u1ec1u h\u01a1n 2, t\u1ed5 ch\u1ee9c tr\u1ed3ng cây. L\u1edbp th\u1ee9 nh\u1ea5t tr\u1ed3ng 5 cây và <span class=\"math-tex\">$\\dfrac{1}{5}$<\/span> s\u1ed1 cây còn l\u1ea1i. L\u1edbp th\u1ee9 hai tr\u1ed3ng ti\u1ebfp 10 cây và <span class=\"math-tex\">$\\dfrac{1}{5}$<\/span> s\u1ed1 cây còn l\u1ea1i. L\u1edbp th\u1ee9 ba tr\u1ed3ng ti\u1ebfp 15 cây và <span class=\"math-tex\">$\\dfrac{1}{5}$<\/span> s\u1ed1 cây còn l\u1ea1i. C\u1ee9 tr\u1ed3ng nh\u01b0 v\u1eady \u0111\u1ebfn l\u1edbp cu\u1ed1i cùng thì v\u1eeba h\u1ebft s\u1ed1 cây và s\u1ed1 cây m\u1ed7i l\u1edbp tr\u1ed3ng \u0111\u01b0\u1ee3c là b\u1eb1ng nhau. Tính s\u1ed1 cây mà kh\u1ed1i 9 tr\u1ed3ng và s\u1ed1 l\u1edbp 9 c\u1ee7a kh\u1ed1i tham gia tr\u1ed3ng cây.<\/p>","options":["<strong>A.<\/strong> 80 cây, 5 l\u1edbp","<strong>B.<\/strong> 80 cây, 4 l\u1edbp","<strong>C.<\/strong> 90 cây, 5 l\u1edbp","<strong>D.<\/strong> 4 l\u1edbp 90 cây"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 80 cây, 4 l\u1edbp.<\/span><\/p><p>G\u1ecdi s\u1ed1 l\u1edbp 9 tham gia tr\u1ed3ng cây là y. \u0110i\u1ec1u ki\u1ec7n: y ∈ \u2115, y > 2.<\/p><p>Do l\u1edbp cu\u1ed1i cùng tr\u1ed3ng h\u1ebft s\u1ed1 cây nên l\u1edbp cu\u1ed1i cùng tr\u1ed3ng \u0111\u01b0\u1ee3c 5y + 0 (cây).<\/p><p>Do s\u1ed1 cây m\u1ed7i l\u1edbp tr\u1ed3ng nh\u01b0 nhau nên m\u1ed7i l\u1edbp \u0111\u1ec1u tr\u1ed3ng 5y cây.<\/p><p>V\u1eady y l\u1edbp tr\u1ed3ng t\u1ea5t c\u1ea3 là 5y² cây.<\/p><p>S\u1ed1 cây l\u1edbp th\u1ee9 nh\u1ea5t tr\u1ed3ng là <span class=\"math-tex\">$5+\\dfrac{5y^2-5}{5}=y^2+4$<\/span>.<\/p><p>Ta có ph\u01b0\u01a1ng trình <span class=\"math-tex\">$y^2+4=5y$<\/span> hay <span class=\"math-tex\">$y^2-5y+4=0$<\/span>.<\/p><p><span class=\"math-tex\">$\\Delta=25-4.1.4=9$<\/span> > 0.<\/p><p>Suy ra ph\u01b0\u01a1ng trình có hai nghi\u1ec7m phân bi\u1ec7t y = 4; y = 1.<\/p><p>K\u1ebft h\u1ee3p \u0111i\u1ec1u ki\u1ec7n có y = 4.<\/p><p>V\u1eady s\u1ed1 cây tr\u1ed3ng là 5.4² = 80 cây và có 4 l\u1edbp 9 tham gia tr\u1ed3ng cây.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-27 08:07:35","option_type":"txt","len":2},{"id":"8878","post_id":"8076","mon_id":"1159278","chapter_id":"1159330","question":"<p>Cho <span class=\"math-tex\">$c=\\sqrt[3]{6\\sqrt{3}+10}$<\/span>, <span class=\"math-tex\">$d=\\sqrt[3]{6\\sqrt{3}-10}$<\/span>. Bi\u1ebft c², d² là nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$X^2+AX+B=0$<\/span>. Ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh \u0111úng.<\/p>","options":["<strong>A.<\/strong> A là s\u1ed1 t\u1ef1 nhiên, B là s\u1ed1 nguyên.","<strong>B.<\/strong> A không là s\u1ed1 t\u1ef1 nhiên, B là s\u1ed1 nguyên.","<strong>C.<\/strong> A không là s\u1ed1 nguyên, B là s\u1ed1 nguyên.","<strong>D.<\/strong> A là s\u1ed1 nguyên, B là s\u1ed1 nguyên."],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> A là s\u1ed1 nguyên, B là s\u1ed1 nguyên.<\/span><\/p><p>Ta có <span class=\"math-tex\">$c^2=\\sqrt[3]{208+120\\sqrt{3}}=\\sqrt[3]{(4+2\\sqrt{3})^3}=4+2\\sqrt{3}$<\/span> ; <\/p><p> <span class=\"math-tex\">$d^2=\\sqrt[3]{208-120\\sqrt{3}}=\\sqrt[3]{(4-2\\sqrt{3})^3}=4-2\\sqrt{3}$<\/span>.<\/p><p>Suy ra <span class=\"math-tex\">$c^2+d^2=8;c^2.d^2=16-12=4$<\/span>.<\/p><p>Do \u0111ó <span class=\"math-tex\">$c^2,d^2$<\/span> là hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$X^2-8X+4=0$<\/span>.<\/p><p>V\u1eady A = –8 là s\u1ed1 nguyên và B = 4 là s\u1ed1 nguyên.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-27 08:17:33","option_type":"txt","len":3},{"id":"8879","post_id":"8076","mon_id":"1159278","chapter_id":"1159330","question":"<p>Gi\u1ea3 s\u1eed <span class=\"math-tex\">$x_1$<\/span>, <span class=\"math-tex\">$x_2$<\/span> là hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$x^2-5x+3=0$<\/span>. Tính <span class=\"math-tex\">$C=\\dfrac{1}{x_1^4}+\\dfrac{1}{x_2^4}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{334}{81}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{334}{18}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{343}{81}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{343}{18}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{343}{81}$<\/span>.<\/span><\/p><p>Ta có <span class=\"math-tex\">$\\Delta=13>0$<\/span> nên ph\u01b0\u01a1ng trình có hai nghi\u1ec7m phân bi\u1ec7t <span class=\"math-tex\">$x_1,x_2$<\/span>.<\/p><p>Áp d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta có <span class=\"math-tex\">$x_1+x_2=5;x_1x_2=3$<\/span>.<\/p><p>Suy ra <span class=\"math-tex\">$x_1^2+x_2^2=(x_1+x_2)^2-2x_1x_2=5^2-2.3=19$<\/span>.<\/p><p><span class=\"math-tex\">$C=\\dfrac{1}{x_1^4}+\\dfrac{1}{x_2^4}=\\dfrac{x_1^4+x_2^4}{(x_1x_2)^4}=\\dfrac{(x_1^2+x_2^2)^2-2(x_1x_2)^2}{(x_1x_2)^4}=\\dfrac{19^2-2.3^2}{3^4}=\\dfrac{343}{81}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-27 08:27:46","option_type":"math","len":0}]}