已知x/y=8,求x^2-3xy+2y^2/x^2-5xy+4y^2的值.
问题描述：
已知x/y=8,求x^2-3xy+2y^2/x^2-5xy+4y^2的值.
答
x^2-3xy+2y^2/x^2-5xy+4y^2
=(x-y)(x-2y)/(x-y)(x-4y)
=(x-2y)/(x-4y)
由x/y=8得
x=8y
带入得:
(x-2y)/(x-4y)
=(8y-2y)/(8y-4y)
=6y/4y
=1.5
答
由于x/y=8,x＝8y且Y不等于0,
（x^2-3xy+2y^2）/（x^2-5xy+4y^2）
＝(X-Y)(X-2Y)/(X-Y)(X-4Y)
=(X-2Y)/(X-4Y)
所以上式为
(8Y-2Y)/(8Y-4Y)=6/4=3/2=1.5