数学问题:分母有理化:1/[9^(1/3)+6^(1/3)+4^(1/3)]

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数学问题:分母有理化:1/[9^(1/3)+6^(1/3)+4^(1/3)]
数学问题:分母有理化:1/[9^(1/3)+6^(1/3)+4^(1/3)]

数学问题:分母有理化:1/[9^(1/3)+6^(1/3)+4^(1/3)]
1/[9^(1/3)+6^(1/3)+4^(1/3)]
= 1/[3^(2/3)+6^(1/3)+2^(2/3)]
分子分母同乘以 (3^(1/3)-2^(1/3))
则分母变为
(3^(1/3)-2^(1/3))[3^(2/3)+6^(1/3)+2^(2/3)]
= 3^(3/3)-2^(3/3))
= 3 - 2
= 1
所以,原式 = 3^(1/3)-2^(1/3)