若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值

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若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy

若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值
若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值

若(x+y)^2=8,(x-y)^2=2,求x^2+y^2及xy的值
(x+y)^2+(x-y)^2
=x^2+2xy+y^2+x^2-2xy+y^2
=2(x^2+y^2)=8+2=10
x^2+y^2=5
(x+y)^2-(x-y)^2
=x^2+2xy+y^2-x^2+2xy-y^2
=4xy=8-2=6
xy=3/2

∵(x+y)²=8
∴x²+2xy+y²=8…………①
∵(x-y)²=2
∴x²-2xy+y²=2…………②
①+②得
2(x²+y²)=10
x²+y²=5
①-②得
4xy=6
xy=1.5
∴x²+y&...

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∵(x+y)²=8
∴x²+2xy+y²=8…………①
∵(x-y)²=2
∴x²-2xy+y²=2…………②
①+②得
2(x²+y²)=10
x²+y²=5
①-②得
4xy=6
xy=1.5
∴x²+y²=5，xy=1.5

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分别展开这两个公式(x+y)^2=8,(x-y)^2=2,
(x+y)^2=8展开得，x^2+2xy+y^2=8
(x-y)^2=2,展开得，x^2-2xy+y^2=2
把两个展开式相加得，2（x^2+y^2）=10，得，x^2+y^2=5
把两个展开式相减得4xy=6,得xy=3/2

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