若x²-6xy+8y²=0(XY≠0)则x:y=

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若x²-6xy+8y²=0(XY≠0)则x:y=若x²-6xy+8y²=0(XY≠0)则x:y=若x²-6xy+8y²=0(XY≠0)则x:

若x²-6xy+8y²=0(XY≠0)则x:y=
若x²-6xy+8y²=0(XY≠0)则x:y=

若x²-6xy+8y²=0(XY≠0)则x:y=
因式分解,x^2-6xy+8y^2=(x-2y)(x-4y)=0
所以x=2y或x=4y
所以x/y=2 或x/y=4

方程两边同除以xy,得(x/y)-6+8(y/x)=0,设k=x/y,即:k-6+8/k=0,因为xy不等于零,所以k=2或4,即为所求。

x²-6xy+(3y)²=y²
(x-3y)²=y²
|x-3y|=y
若x-3y=y
x=4y
x:y=4:1

若x-3y=-y
x=2y
x:y=2:1