要使a^(1/3)-b^(1/3)<(a-b)^(1/3)成立。a .b应满足的条件是
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要使a^(1/3)-b^(1/3)<(a-b)^(1/3)成立
两边立方 化简
(ab)^(1/3)[a^(1/3)-b^(1/3)]>0
解得
a>b
或a<0 b>0
两边立方 化简
(ab)^(1/3)[a^(1/3)-b^(1/3)]>0
解得
a>b
或a<0 b>0
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a^(1/3)-b^(1/3)<(a-b)^(1/3)
<=> [a^(1/3)-b^(1/3)]³<[(a-b)^(1/3)]³
<=> a - b +3a^(1/3)·b^(2/3) - 3a^(2/3)·b^(1/3) < a - b
<=> 3a^(1/3)·b^(2/3) - 3a^(2/3)·b^(1/3) < 0
<=> a^(1/3)·b^(2/3) < a^(2/3)·b^(1/3)
<=> [a^(1/3)·b^(2/3)]³ < [a^(2/3)·b^(1/3)]³
<=> ab² < a²b
<=> ab² - a²b < 0
<=> ab(b-a) < 0
<=> ab<0, b-a>0 或ab>0, b-a<0
<=> a<0<b 或 a>b>0 或 b<a<0
<=> [a^(1/3)-b^(1/3)]³<[(a-b)^(1/3)]³
<=> a - b +3a^(1/3)·b^(2/3) - 3a^(2/3)·b^(1/3) < a - b
<=> 3a^(1/3)·b^(2/3) - 3a^(2/3)·b^(1/3) < 0
<=> a^(1/3)·b^(2/3) < a^(2/3)·b^(1/3)
<=> [a^(1/3)·b^(2/3)]³ < [a^(2/3)·b^(1/3)]³
<=> ab² < a²b
<=> ab² - a²b < 0
<=> ab(b-a) < 0
<=> ab<0, b-a>0 或ab>0, b-a<0
<=> a<0<b 或 a>b>0 或 b<a<0
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