{"common":{"save":0,"post_id":"7055","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4933","post_id":"7055","mon_id":"1158924","chapter_id":"1159147","question":"<p>Cho dãy s\u1ed1 <span class=\"math-tex\">$(u_n)$<\/span>, bi\u1ebft <span class=\"math-tex\">$u_n=(-1)^n.2n$<\/span> . M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây là <strong>sai<\/strong>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$u_1=-2$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$u_2=4$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$u_3=-6$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$u_4=-8$<\/span>"],"correct":"4","level":"2","hint":"<p> <span class=\"math-tex\">$u_4=(-1)^4.2.4=8$<\/span> <\/p>","answer":"<p>Ta có <span class=\"math-tex\">$u_4=(-1)^4.2.4=8$<\/span> <\/p><p>Do \u0111ó ph\u01b0\u01a1ng án sai là <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$u_4=-8$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-13 02:25:54","option_type":"math","len":0},{"id":"4935","post_id":"7055","mon_id":"1158924","chapter_id":"1159147","question":"<p>V\u1edbi giá tr\u1ecb nào c\u1ee7a <span class=\"math-tex\">$n$<\/span> thì 3 s\u1ed1 <span class=\"math-tex\">$3;n;3n-1$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 c\u1ed9ng?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$n=2$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$n=-2$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$n=1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$n=\\dfrac{4}{3}$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 ba s\u1ed1 <span class=\"math-tex\">$3;n;3n-1$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 c\u1ed9ng là<\/p><p><span class=\"math-tex\">$n-3=3n-1-n$<\/span> ⇔ <span class=\"math-tex\">$n=-2$<\/span> .<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$n=-2$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-13 02:28:40","option_type":"math","len":0},{"id":"4938","post_id":"7055","mon_id":"1158924","chapter_id":"1159147","question":"<p>Xét các s\u1ed1 th\u1ef1c d\u01b0\u01a1ng <span class=\"math-tex\">$a,b$<\/span> sao cho <span class=\"math-tex\">$-25;2a;3b$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 c\u1ed9ng và <span class=\"math-tex\">$2;a+2;b-3$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 nhân. Khi \u0111ó <span class=\"math-tex\">$a^2+b^2-3ab$<\/span> b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> 59","<strong>B.<\/strong> 89","<strong>C.<\/strong> 31","<strong>D.<\/strong> 76"],"correct":"1","level":"2","hint":"","answer":"<p>Vì <span class=\"math-tex\">$-25;2a;3b$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 c\u1ed9ng nên <\/p><p><span class=\"math-tex\">$-25+3b=4a$<\/span> ⇒ <span class=\"math-tex\">$3b-9=4a+16$<\/span> .<\/p><p>Vì <span class=\"math-tex\">$2;a+2;b-3$<\/span> theo th\u1ee9 t\u1ef1 l\u1eadp thành c\u1ea5p s\u1ed1 nhân nên <span class=\"math-tex\">$2.(b-3)=(a+2)^2$<\/span> .<\/p><p>Suy ra <span class=\"math-tex\">$2.\\dfrac{4a+16}{3}=(a+2)^2$<\/span> ⇔ <span class=\"math-tex\">$2.(4a+16)=3.(a+2)^2$<\/span> ⇔ <span class=\"math-tex\">$3a^2+4a-20=0$<\/span><\/p><p>Vì <span class=\"math-tex\">$a>0$<\/span> nên <span class=\"math-tex\">$a=2$<\/span> suy ra <span class=\"math-tex\">$b=11$<\/span> .<\/p><p>V\u1eady <span class=\"math-tex\">$a^2+b^2-3ab=4+121-3.2.11=59$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 59.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-13 02:36:26","option_type":"txt","len":0}]}