已知(x+y)²=25,(x-y)²=9,求xy与x²+y²的值
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已知(x+y)²=25,(x-y)²=9,求xy与x²+y²的值
已知(x+y)²=25,(x-y)²=9,求xy与x²+y²的值
已知(x+y)²=25,(x-y)²=9,求xy与x²+y²的值
(x+y)²=25
x²+y²+2xy=25——①
(x-y)²=9
x²+y²-2xy=9——②
①-②:4xy=25-9=16
xy=4
①+②:2(x²+y²)=34
x²+y²=17
(x+y)²=25,x²+2xy+y²=25
(x-y)²=9,x²-2xy+y²=9
两式相加,2(x²+y²)=34
所以,x²+y²=17