Question

已知实数a,b满足(a+b)2=1,(a-b)2=25，求a2+b2+ab的值.

Answer 1

(a+b)2-(a-b)2=4ab=1-25=-24
ab=-24/4=-6
a2+b2=(a+b)2-2ab

a2+b2+ab
=(a+b)2-2ab+ab
=1-(-6)
=7

Answer 2

（a-b)^2-(a+b)^2=25-1
a^2-2ab+b^2-a^2-2ab-b^2=24
-4ab=24
ab=-6

a^2+b^2+ab=a^2+2ab+b^2-an=(a+b)^2-ab=1-(-6)=7