若12X^2+12Y^2=25XY,试求X/Y的值

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若12X^2+12Y^2=25XY,试求X/Y的值
若12X^2+12Y^2=25XY,试求X/Y的值

若12X^2+12Y^2=25XY,试求X/Y的值
12X^2+12Y^2=25XY
即：12x^2-25xy+12y^2=0
十字相乘分解因式得：(4x-3y)(3x-4y)=0
所以4x-3y=0或3x-4y=0
即x/y=3/4或x/y=4/3

两边同时除以y^2就可以了然后解个一元二次方程就可以了~~~

两边同除以12*y*y
令x/y=a
a*a+1=25/12a
a=(25/12+7/12)/2=8/3,
a=(25/12-7/12)/2=3/4

12/13

12x^2+12y^2=25xy
(12x^2+12y^2)/y^2=25xy/y^2
12(x/y)^2-25(x/y)+12=0
(x/y)=[25±√(25^2-4*12*12)]/(2*12)
=(25±7)/24
(x/y)=(4/3),(3/4)

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