已知(x-y)(y+x)=xy 求x∕y+y∕x=?求具体过程.
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已知(x-y)(y+x)=xy 求x∕y+y∕x=?求具体过程.
由(a+b)²=(a-b)²+4ab可得答案.
∵(x-y)(y+x)=xy
∴x²-y²=xy
两边同除以xy,得
x/y-y/x=1
(x∕y+y∕x)²=(x/y-y/x)²+4*(x/y·y/x)=1+4=5
故x/y+y/x=±√5
故答案是:±√5
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∵(x-y)(y+x)=xy
∴x²-y²=xy
两边同除以xy,得
x/y-y/x=1
(x∕y+y∕x)²=(x/y-y/x)²+4*(x/y·y/x)=1+4=5
故x/y+y/x=±√5
故答案是:±√5
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