Question

（1）已知（a+b）^2=7，(a-b）^2=4，求a^2+b^2和ab的值（2）已知a-1/a=4，求a^2+1/a^2的值

Answer 1

(1)解：（a+b）^2-(a-b）^2=a^2+b^2-a^2-b^2+2ab+2ab=4ab=7-4=3 ab=3\4 （a+b）^2=a^2+b^2+2ab=7 a^2+b^2=7-2ab=7-2*3\4=7-11\2(2)解：（a-1/a)^2=a^2+1/a^2+2*a*1\a=a^2+1/a^2+2=4^2=16 a^2+1/a^2=16-2=14

Answer 2

(a+b)^2=7 a^2+b^2+2ab=7(a-b)^2=4 a^2+b^2-2ab=4两式相加 a^2+b^2=11/2两式相减 ab=3/4 a-1/a=4(a-1/a)^2=16a^2+1/a^2-2=16a^2+1/a^2=18