If x=5^{1{/}3}+5^{-1{/}3},then 5x^3-15x=

NIFT UG 2015 Question Paper with solutions

Question : 59 of 150

Marks: +1, -0

x=5^{1{/}3}+5^{-1{/}3}

,then

5x^3-15x=

Solution:

X=5^{1/3}+5^{-1/3}

X^3=(5^{1/3}+5^{-1/3})^3

=5+1/5+3(5^{1/3}+5^{-1/3})

=26/5+3(5^{1/3}+5^{-1/3})

=26/5++3(5^{1/3}+5^{-1/3})

Now,

5X^{3}-15X

=5(\;\;{26}/{5}+3(5^{\;\;{1}/{3}}+5^{-\;\;{1}/{3}}))-15(5^{\;\;{1}/{3}}+5^{-\;\;{1}/{3}})

=26+15(5^{\;\;{1}/{3}}+5^{-\;\;{1}/{3}})-15(5^{\;\;{1}/{3}}+5^{-\;\;{1}/{3}})

=26

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