已知2x-y=10,求代数式[(x的2次方+y的2次方)-(x-y)的2次方+2y(x-y)]÷4y的值.
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已知2x-y=10,求代数式[(x的2次方+y的2次方)-(x-y)的2次方+2y(x-y)]÷4y的值.
![已知2x-y=10,求代数式[(x的2次方+y的2次方)-(x-y)的2次方+2y(x-y)]÷4y的值.](/uploads/image/z/14182248-48-8.jpg?t=%E5%B7%B2%E7%9F%A52x-y%3D10%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%5B%28x%E7%9A%842%E6%AC%A1%E6%96%B9%2By%E7%9A%842%E6%AC%A1%E6%96%B9%29-%28x-y%29%E7%9A%842%E6%AC%A1%E6%96%B9%2B2y%28x-y%29%5D%C3%B74y%E7%9A%84%E5%80%BC.)
2x - y = 10
[(x^2 + y^2) - (x - y)^2 + 2y(x - y)]/(4y)
= [(x^2 + y^2) - (x^2 - 2xy + y^2) + 2y(x - y)]/(4y)
= [2xy + 2y(x - y)]/(4y)
= [2y(2x - y)]/(4y)
= (2x - y)/2
= 5
[(x^2 + y^2) - (x - y)^2 + 2y(x - y)]/(4y)
= [(x^2 + y^2) - (x^2 - 2xy + y^2) + 2y(x - y)]/(4y)
= [2xy + 2y(x - y)]/(4y)
= [2y(2x - y)]/(4y)
= (2x - y)/2
= 5
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