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高中课本第二册P88的例3是有关最值的一个例题,题目为: “己知x,y∈R~+,x+y=S,x·y=P,求证: ①如果P的定值,那么当且仅当x=y时,S的值最小。(2(p)~(1/2)) ②如果S是定值,那么当且仅当x=y时,P的值最大。(S~2/4) 事实上,上述结论包含在恒等式xy=(x+y)~2-(x-y)~2/4(x,y∈R~+,x≥y)中,如果我们认真分析恒等式xy=(x+y)~2-(x-y)~2/(4)x、y ∈R~+,x≥y,便可得到如下的结论。 (1)当积xy为定值时,和x+y的值随差x -y的增大而增大。当且仅当差x-y取得最
Example 3 of the high school textbook second volume P88 is an example of the most relevant value. The title is: “Know x, y∈R~+, x+y=S, x•y=P, verify: 1 If P Value, then if and only if x = y, the value of S is the smallest (2(p) ~ (1/2)) 2 If S is a fixed value, then if and only if x = y, the value of P is maximum (S~2/4) In fact, the above conclusion is included in the identity xy=(x+y)~2-(xy)~2/4(x,y∈R~+,x≥y) if we Carefully analyzing the identities xy=(x+y)~2-(xy)~2/(4)x, y ∈R~+, x≥y, we can get the following conclusions: (1) When product xy is constant When, the value of x and y increases with the difference x -y, if and only if the difference xy gets the most