求证x^3+y^3-3x^2y+xy^2≥0x,y,z均为正实数_数学解答

求证x^3+y^3-3x^2y+xy^2≥0
x,y,z均为正实数

人气：401 ℃　时间：2020-03-22 06:06:57

解答

x³+y³-3x²y+xy²
=x³-x²y-xy²+y³-2x²y+2xy²
=(x-y)(x²-y²)-2xy(x-y)
=(x-y)(x²-2xy-y²)
所以原式有反例,
x=2,y=1