矩形的周长是28cm,两边分别为xcm、ycm,若x^3+x^2y-xy^2-y^3=0,求矩形的面积\_数学解答

矩形的周长是28cm,两边分别为xcm、ycm,若x^3+x^2y-xy^2-y^3=0,求矩形的面积\

人气：365 ℃　时间：2020-04-15 18:36:09

解答

x^3+x^2y-xy^2-y^3
=(x^3-y^3)+(x^2y-xy^2)
=(x-y)(x^2+xy+y^2)+xy(x-y)
=(x-y)(x^2+2xy+y^2)
=(x-y)(x+y)^2
=0
x+y=28/2=14
x-y=0
x=y=7
矩形面积xy=49