已知(a+b)^2=6,(a-b)^2=3,则2a^2-3ab+2b^2

题目

已知(a+b)^2=6,(a-b)^2=3,则2a^2-3ab+2b^2
如题

答案

(a+b)^2-(a-b)^2=6-3=3=4ab
ab=3/4
2a^2-3ab+2b^2
=2a^2-4ab+2b^2+ab
=2(a-b)^2+ab
=2×3+3/4
=6又3/4