已知x,y是正数,求证:(x+y)(x^2+y^2)(x^3+y^3)>=8x^3y^3
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 20:02:04
![已知x,y是正数,求证:(x+y)(x^2+y^2)(x^3+y^3)>=8x^3y^3](/uploads/image/z/14856053-5-3.jpg?t=%E5%B7%B2%E7%9F%A5x%2Cy%E6%98%AF%E6%AD%A3%E6%95%B0%2C%E6%B1%82%E8%AF%81%EF%BC%9A%28x%2By%29%28x%5E2%2By%5E2%29%28x%5E3%2By%5E3%29%3E%3D8x%5E3y%5E3)
已知x,y是正数,求证:(x+y)(x^2+y^2)(x^3+y^3)>=8x^3y^3
已知x,y是正数,求证:(x+y)(x^2+y^2)(x^3+y^3)>=8x^3y^3
已知x,y是正数,求证:(x+y)(x^2+y^2)(x^3+y^3)>=8x^3y^3
首先(x+y)(x^2+y^2)(x^3+y^3)=(x+y)^2(x^2+y^2)(x^2-xy+y^2)
因为x,y都是正数
有(x+y)^2≥4xy
(x^2+y^2)≥2xy
(x^2-xy+y^2)≥xy
三式子相乘
即(x+y)(x^2+y^2)(x^3+y^3)≥8x^3y^3