已知X/Y=2/7,求x^2-3XY+2Y^2/X^2-2XY+Y^2

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已知X/Y=2/7,求x^2-3XY+2Y^2/X^2-2XY+Y^2
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已知X/Y=2/7,求x^2-3XY+2Y^2/X^2-2XY+Y^2
已知X/Y=2/7,求x^2-3XY+2Y^2/X^2-2XY+Y^2

已知X/Y=2/7,求x^2-3XY+2Y^2/X^2-2XY+Y^2
(x^2-3XY+2Y^2)/(X^2-2XY+Y^2)
=(x-2y)(x-y)/(x-y)^2
=(x-2y)/(x-y)
=(x-y-y)/(x-y)
=1- y/(x-y)
=1- 1/(x/y -1)
=1- 1/(2/7 -7/7)
=1+ 1/(5/7)
=1+ 7/5
=12/5

这是齐次式，把分子分母同除以y^2

x^2-3XY+2Y^2/X^2-2XY+Y^2
=(x²-2xy+y²+y²-xy)/(x-y)²
=<(x-y)²+y(y-x)>/(x-y)²
=<(x-y)²-y(x-y)>/(x-y)²
=1-y/(x-y)
=1-y/x+1
=2-y/x
x/y=2/7
y/x=7/2
2-7/2=-3/2

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