若(x+y)^2=10,(x-y)^2=6,求x^2+y^2及xy的值
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若(x+y)^2=10,(x-y)^2=6,求x^2+y^2及xy的值
若(x+y)^2=10,(x-y)^2=6,求x^2+y^2及xy的值
若(x+y)^2=10,(x-y)^2=6,求x^2+y^2及xy的值
解
(x+y)²=10
即x²+y²+2xy=10 ①
(x-y)²=6
即x²+y²-2xy=6 ②
①+②得:
2x²+2y²=16
∴x²+y²=8
①-②得:
4xy=4
xy=1
x2+y2
因为x2+y2+2xy=10
x2+y2-2xy=6
4xy=16
xy=4
x2+y2=10-8=2
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