已知(a+b)눀=7,(a-b)눀=4,求a눀+b눀和ab的值。

2025-06-22 00:32:59
推荐回答(2个)
回答1:

∵(a+b)²+(a-b)²=(a²+b²+2ab)+(a²+b²-2ab)=2a²+2b²=11

∴a²+b²=11/2

∵(a+b)²-(a-b)²=(a²+b²+2ab)-(a²+b²-2ab)=a²+b²+2ab-a²-b²+2ab=4ab=3
∴ab=3/4

回答2:

(a+b)²+(a-b)²=a²+b²+2ab+a²+b²-2ab=2a²+2b²=11 ->a²+b²=11/2

(a+b)²-(a-b)²=a²+b²+2ab-a²-b²+2ab=4ab=3 -> ab=3/4