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已知a=³√4+³√2+1,求3\a+3\a²+1\a³
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a=³√4+³√2+³√1
a-1=³√4+³√2
两边三次方得:
a^3-3a^2+3a-1=6+6³√4+6³√2
a^3-3a^2+3a-1=6+6(³√4+³√2)
a^3-3a^2+3a-1=6+6(a-1)
a^3-3a^2-3a-1=0
a^3=3a^2+3a+1
1/a³+3/a²+3/a
=(3a^2+3a+1)/a^3
=a^3/a^3
=1
a-1=³√4+³√2
两边三次方得:
a^3-3a^2+3a-1=6+6³√4+6³√2
a^3-3a^2+3a-1=6+6(³√4+³√2)
a^3-3a^2+3a-1=6+6(a-1)
a^3-3a^2-3a-1=0
a^3=3a^2+3a+1
1/a³+3/a²+3/a
=(3a^2+3a+1)/a^3
=a^3/a^3
=1
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