证明 所证不等式去分母,化简等价于(2x^2+yz)*(yz+zx+xy)≥9x^2*yz (1)(1)<==>2x^3(y+z)+xyz(y+z)+(yz)^2-7x^2*yz≥0 (2)由均值不等式得x^3*y+x^3*z+(yz)^2≥3x^2*yz (3)x^3*y+xyz^2≥2x^2*yz (4)x^3 展开
证明 所证不等式去分母,化简等价于(2x^2+yz)*(yz+zx+xy)≥9x^2*yz (1)(1)<==>2x^3(y+z)+xyz(y+z)+(yz)^2-7x^2*yz≥0 (2)由均值不等式得x^3*y+x^3*z+(yz)^2≥3x^2*yz (3)x^3*y+xyz^2≥2x^2*yz (4)x^3*z+xzy^2≥3x^2*yz (5) (3)+(4)+(5)即得不等式(2). 收起
