Question

如果X²-3Y²=2XY那么(X+2Y)/X-Y的值是多少

Answer 1

X^2-3Y^2=2XY

x^2-2xy-3y^2=0

(x+y)(x-3y)=0

x+y=0或x-3y=0

x=-y或x=3y

x=-y时,(X+2Y)/X-Y=（-y+2y）/(-y-y)=-1/2

x=3y时,(X+2Y)/X-Y=（3y+2y）/(3y-y)=5/2