已知a+b=6,ab=3求a²-b²= (5ab+4a+7b)+(6a-3ab)-(4ab-3b)=

问题描述:

已知a+b=6,ab=3求a²-b²= (5ab+4a+7b)+(6a-3ab)-(4ab-3b)=

54

a²-b²= (a+b)²-2ab
=6×6-3×2
=30
(5ab+4a+7b)+(6a-3ab)-(4ab-3b)
=5ab+4a+7b+6a-3ab-4ab+3b
=10a+10b+5ab-7ab
=10(a+b)-2ab
=10×6-2×3
=54