Question

已知实数a,b满足(a+b)^2=1,(a-b)^2=25,求a^2+b^2+ab的值

Answer 1

(a+b)^2=a^2+2ab+b^2=1

(a-b)^2=a^2-2ab+b^2=25

两式相加2a^2+2b^2=26

a^2+b^2=13

两式相减4ab=-24

ab=-6

a^2+b^2+ab=7