(a+b)²=12,(a-b)²=4,求(3a-b)²-(2a-b)²+5a(b-a)的值

问题描述:

(a+b)²=12,(a-b)²=4,求(3a-b)²-(2a-b)²+5a(b-a)的值

(3a-b)²-(2a-b)²+5a(b-a)的值
=9a²-6ab+b²-(4a²-4ab+b²)+5ab-5a²
=9a²-6ab+b²-4a²+4ab-b²+5ab-5a²
=3ab
=[(a+b)²-(a-b)²]/4
=(12-4)/4
=2
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