已知x²-xy-2y²=0,(x≠0,y≠0)求(x²-2xy)/(xy+y²)的值
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![已知x²-xy-2y²=0,(x≠0,y≠0)求(x²-2xy)/(xy+y²)的值](/uploads/image/z/1782084-12-4.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B-xy-2y%26%23178%3B%3D0%2C%EF%BC%88x%E2%89%A00%2Cy%E2%89%A00%EF%BC%89%E6%B1%82%EF%BC%88x%26%23178%3B-2xy%EF%BC%89%2F%EF%BC%88xy%2By%26%23178%3B%EF%BC%89%E7%9A%84%E5%80%BC)
已知x²-xy-2y²=0,(x≠0,y≠0)求(x²-2xy)/(xy+y²)的值
已知x²-xy-2y²=0,(x≠0,y≠0)求(x²-2xy)/(xy+y²)的值
已知x²-xy-2y²=0,(x≠0,y≠0)求(x²-2xy)/(xy+y²)的值
∵已知x²-xy-2y²=0 ==>(x+y)(x-2y)=0
∴x+y=0,或x-2y=0
∵(x²-2xy)/(xy+y²) =[x(x-2y)]/[y(x+y)]
∴x+y≠0 (所求分式分母不能为零)
∴x-2y=0 ==>x=2y
故(x²-2xy)/(xy+y²) =[x(x-2y)]/[y(x+y)]
=[2y*0]/[y(2y+y)] (x≠0,y≠0)
=0.