Question

[tex] x^{3} + \frac{1}{ x^{3} } =110 then, x+ \frac{1}{x} will be
[/tex]

Answer 1

x^3 + 1/x^3 = 110 
(x + 1/x)^3 -- 3x(1/x)(x + 1/x) = 110 
(x + 1/x)^3 -- 3(x + 1/x) -- 110 = 0 
Putting (x + 1/x) = A, 
A^3 -- 3A -- 110 = 0 
A^3 -- 5A^2 + 5A^2 -- 25A + 22A -- 110 = 0, from 110 = 22x5 
A^2(A -- 5) + 5A(A -- 5) + 22(A -- 5) = 0 
(A -- 5)(A^2 + 5A + 22) = 0 
whence A -- 5 = 0 OR A = 5 
Giving x + 1/x = 5 ANSWER