已知(a-b)²=7,(a+b)²=13,试求a²+b²和ab的值.
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已知(a-b)²=7,(a+b)²=13,试求a²+b²和ab的值.
已知(a-b)²=7,(a+b)²=13,试求a²+b²和ab的值.
已知(a-b)²=7,(a+b)²=13,试求a²+b²和ab的值.
∵(a-b)²=a²-2ab+b²=7 .(1)
(a+b)²=a²+2ab+b²=13 .(2)
∴(1)+(2),得:2(a²+b²)=20
∴a²+b²=10
∴ab=[(a+b)²-(a²+b²)]/2=3/2
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