设含有变量x1,x2,…,xn的不等式,如果对任意正数λ,用λx1,λx2,…,λxn去替代x1,x2,…,xn所得的不等式不改变,则称这个不等式是齐次不等式,否则,称这个不等式是非齐次不等式.齐次不等式体现了数学的对称美和和谐美,所以我们常常把非齐次不等式转化为齐次不等式进行证明,这样可以化繁为简,达到事半功倍的效果.反过来,对于某些齐次不等式,如果我们增加条件将它非齐次化,有时也会减少不必要的复 Suppose the inequality containing the variables x1, x2, ..., xn is inequality if the inequality obtained by replacing x1, x2, ..., xn by λx1, λx2, ..., λxn for any positive number λ is not changed, Inequality, otherwise, we call this inequality inequality inequality. Homogeneity inequality embodies the symmetry beauty and harmony beauty of mathematics, so we often prove that nonhomogeneous inequality is transformed into homogeneous inequality so that it can be simplified and multiplied Conversely, for some homogeneous inequalities, if we add conditions to non-homogeneous and sometimes reduce unnecessary complexities