若(a+b)²=1(a-b)²=25求a²+b²,ab
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若(a+b)²=1(a-b)²=25求a²+b²,ab
若(a+b)²=1(a-b)²=25求a²+b²,ab
若(a+b)²=1(a-b)²=25求a²+b²,ab
解
(a+b)²=1
a²+2ab+b²=1 ①
(a-b)²=25
a²-2ab+b²=25 ②
①+②得
2a²+2b²=26
∴a²+b²=13
①-②得:
4ab=-24
∴ab=-6
答:
(a+b)²=1,a²+2ab+b²=1
(a-b)²=25,a²-2ab+b²=25
两式相加得:
2(a²+b²)=26
a²+b²=13
两式相减得:
4ab=-24
ab=-6
综上所述:a²+b²=26,ab=-6