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已知x^2+y^2=6xy,且x＞y＞0,求x-y/x+y
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已知x^2+y^2=6xy,且x＞y＞0,求x-y/x+y
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答案和解析
x²+y²=6xy
x²+y²+2xy=8xy ,x²+y²-2xy=4xy
(x+y)²=8xy, (x-y)²=4xy
∴ (x-y)²/(x+y)²=4/8=1/2
∵ x>y>0
∴ (x-y)/(x+y)=√2/2
x²+y²=6xy
x²+y²+2xy=8xy ,x²+y²-2xy=4xy
(x+y)²=8xy, (x-y)²=4xy
∴ (x-y)²/(x+y)²=4/8=1/2
∵ x>y>0
∴ (x-y)/(x+y)=√2/2
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