若x>0,y>0,且x+√xy-2y=0,则代数式(2x-3y)(3x+2y)(x^3-y^3)-1的立方根是
问题描述:
若x>0,y>0,且x+√xy-2y=0,则代数式(2x-3y)(3x+2y)(x^3-y^3)-1的立方根是
答
将x+√xy-2y=0,转化为√xy=2y-x.方程两边平方后得4y^2+x^2-5xy=0.解得x=y或x=4y.根据x>0,y>0,代入判定若x=4y,则√xy=2y-x=2y-4y=-2y