已知x^2+y^2-10x-12y+61=0,求x/y-y/x的值
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已知x^2+y^2-10x-12y+61=0,求x/y-y/x的值
x^2+y^2-10x-12y+61=0
(x²-10x+25)+(y²-12y+36)=0
(x-5)²+(y-6)²=0
因为(x-5)²与(y-6)²分别≥0
要想(x-5)²+(y-6)²=0,必然
(x-5)²=0
x-5=0
x=5
(y-6)²=0
y-6=0
y=6
x/y-y/x
=5/6-6/5
=﹣11/30
(x²-10x+25)+(y²-12y+36)=0
(x-5)²+(y-6)²=0
因为(x-5)²与(y-6)²分别≥0
要想(x-5)²+(y-6)²=0,必然
(x-5)²=0
x-5=0
x=5
(y-6)²=0
y-6=0
y=6
x/y-y/x
=5/6-6/5
=﹣11/30
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