代数式求值 x÷3y=y÷2x-5y=6x-15y÷x 求4x²-5xy+6y²÷x²-2xy+3y²

Question

x÷3y=y÷2x-5y=6x-15y÷x
求4x²-5xy+6y²÷x²-2xy+3y²

Answer 1

x/3y=y/2x-5y
2x^2-5xy-3y^2=0
(x-3y)(2x+y)=0①
x/3y=6x-15y/x
x^2-18xy+45y^2=0
(x-3y)(x-15y)=0②
y/2x-5y=6x-15y/x
xy=3(2x-5y)^2
(x-3y)(12x-25)=0③
若①②③同时成立，
x-3y=0,x=3y
(4x^2-5xy+6y^2)/(x^2-2xy+3y^2)
=[4(3y)^2-5*(3y)*y+6y^2]/[(3y)^2-2*(3y)*y+3y^2]
=9/2

Answer 2

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