题目内容
若x＜y＜0,试比较(x2+y2)(x-y)与(x2-y2)(x+y)的大小.
解析:(用作差法比较)
(x2+y2)(x-y)-(x2-y2)(x+y)
=(x-y)［(x2+y2)-(x+y)2］=-2xy(x-y).
∵x＜y＜0,∴xy＞0,x-y＜0.
∴-2xy(x-y)＞0.
∴(x2+y2)(x-y)＞(x2-y2)(x+y).
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题目内容
若x＜y＜0,试比较(x2+y2)(x-y)与(x2-y2)(x+y)的大小.
解析:(用作差法比较)
(x2+y2)(x-y)-(x2-y2)(x+y)
=(x-y)［(x2+y2)-(x+y)2］=-2xy(x-y).
∵x＜y＜0,∴xy＞0,x-y＜0.
∴-2xy(x-y)＞0.
∴(x2+y2)(x-y)＞(x2-y2)(x+y).
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