逆用无穷等比数列各项和公式可化复杂不等式为平凡不等式.例1设x,y,z0,则x2-z2y+z+yz2-+xx2+zx2-+yy2≥0(W.Janous猜测)证明令x+y+z=s,则不等式的左边等于x2-z2s-x+ys2--yx2+zs2--yz2=1s(1x2--sxz2+y12--syx2+z12--syz2)=1s[(x2-z2)(1+sx+xs22+…)+(y2-x2)(1+sy+sy22+…)+(z2- Inverse multiples of infinite series of equations and formulas can be complicated inequality is trivial inequality. Example 1 set x, y, z0, then x2-z2y + z + yz2- + xx2 + zx2- + yy2 ≥ 0 (W. Janous guess ) Let x + y + z = s prove that the left side of the inequality is equal to x2-z2s-x + ys2-yx2 + zs2- yz2 = 1s (1x2- sxz2 + y12- syx2 + z12- syz2) = 1s [(x2-z2) (1 + sx + xs22 + ...) + (y2-x2) (1 + sy + sy22 + ...) + (z2-