x^2-7xy+12y^2=0，求x^2-2xy+y^2/2xy的值
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x^2-7xy+12y^2=0
(x-3y)(x-4y)=0
x=3y或x=4y
当x=3y时
(x^2-2xy+y^2)/2xy
=(x-y)^2/2xy
=(3y-y)^2/2*3y*y
=4y^2/6y^2
=4/6
=2/3
当x=4y时
(x^2-2xy+y^2)/2xy
=(x-y)^2/2xy
=(4y-y)^2/2*4y*y
=9y^2/8y^2
=9/8
(x-3y)(x-4y)=0
x=3y或x=4y
当x=3y时
(x^2-2xy+y^2)/2xy
=(x-y)^2/2xy
=(3y-y)^2/2*3y*y
=4y^2/6y^2
=4/6
=2/3
当x=4y时
(x^2-2xy+y^2)/2xy
=(x-y)^2/2xy
=(4y-y)^2/2*4y*y
=9y^2/8y^2
=9/8
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x^2-7xy+12y^2=0==>(X-3Y)(X-4Y)=0==>X=3Y 或者X=4Y
当X=3Y
x^2-2xy+y^2/2xy=((3Y)^2-2*3Y*Y+Y^2)/(2*3Y*Y)=4Y^2/6Y^2=2/3
当X=4Y
x^2-2xy+y^2/2xy=((4Y)^2-2*4Y*Y+Y^2)/(2*4Y*Y)=9Y^2/8Y^2=9/8
所以x^2-2xy+y^2/2xy值为2/3或者9/8
当X=3Y
x^2-2xy+y^2/2xy=((3Y)^2-2*3Y*Y+Y^2)/(2*3Y*Y)=4Y^2/6Y^2=2/3
当X=4Y
x^2-2xy+y^2/2xy=((4Y)^2-2*4Y*Y+Y^2)/(2*4Y*Y)=9Y^2/8Y^2=9/8
所以x^2-2xy+y^2/2xy值为2/3或者9/8
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