Let `a` is a real number satisfying `a^3+1/(a^3)=18` . Then the value of `a^4+1/(a^4)-39` is ____.

Answer

`a^(4) + (1)/(a^(4)) = 47`

Explanation

Let ` a + (1)/(a) = t`
`therefore t^(3) - 3t - 18 = 0`
t - 3 satisfies this equation
`therefore (t - 3 ) (t^(2) _ 3t + 6 ) = 0`
Clearly, t = 3 is the only soultion
`therefore a ^(2) + (1)/(a) = 3`
`rArr a^(2) + (1)/(a^(2)) = 7`
`rArr a^(4) + (1)/(a^(4)) = 47` .