已知x,y都是正数,求证:(x+y)(x^+y^)(x^3+y^3）≥8x^3y^3

已知x,y都是正数,求证:(x+y)(x^+y^)(x^3+y^3）≥8x^3y^3
已知x,y都是正数,求证:(x+y)(x^+y^)(x^3+y^3）≥8x^3y^3

已知x,y都是正数,求证:(x+y)(x^+y^)(x^3+y^3）≥8x^3y^3
x,y都是正数,所以
x+y≥2(xy)^(1/2)
x^2+y^2≥2xy
x^3+y^3≥2(xy)^(3/2)
三式相乘
便得:(x+y)(x^+y^)(x^3+y^3）≥8x^3y^3