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相等与不等是一对矛盾,它们在一定条件下可以相互转换,有些数学问题如果只在相等或不等方面作文章,往往劳而无功,这时若考虑相等与不等之间的相互转换,常可使问题迎刃而解。例1 已知实数x,y,z,s满足x+y+z+s=a(a＞0),求证：x~2+y~2+z~2+s~2≥a~2/4。证明设x=a/4+α,y=a/4+β,z=a/4+γ,s=a/4+δ,其中α,β,γ,δ都称为增量,这里α+β+γ+δ=0。
Equivalence and inequality are contradictory, and they can be converted to each other under certain conditions. If some mathematics problems are only essayed in terms of equality or inequality, they are often laborious and inefficient. At this time, if equal or inequality is considered Conversion can often solve the problem. Example 1 Known real numbers x, y, z, s satisfy x + y + z + s = a (a> 0). Proof: x~2+y~2+z~2+s~2≥a~2/ 4. Proof Let x = a / 4 + α, y = a / 4 + β, z = a / 4 + γ, s = a / 4 + δ, where α, β, γ, δ are called increments, where α +β+γ+δ=0.