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x^2-y^2=2xy求（x-y)/(x+y)=?
题目详情
x^2-y^2=2xy 求（x-y)/(x+y)=?
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答案和解析
x²-y²=2xy
(x²-y²)²=(2xy)²
x^4-2x²y²+y^4=4x²y²
x^4+2x²y²+y^4=8x²y²
(x²+y²)²=8x²y²
x²+y²=±2√2xy
（x-y)/(x+y)=(x²-y²)/(x+y)²=2xy/(x²+y²+2xy)=2xy/(±2√2xy+2xy)
=1/(1±√2)
=±√2-1
(x²-y²)²=(2xy)²
x^4-2x²y²+y^4=4x²y²
x^4+2x²y²+y^4=8x²y²
(x²+y²)²=8x²y²
x²+y²=±2√2xy
（x-y)/(x+y)=(x²-y²)/(x+y)²=2xy/(x²+y²+2xy)=2xy/(±2√2xy+2xy)
=1/(1±√2)
=±√2-1
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