Question

If $x+\frac{1}{x}=4$ then $x^5+\frac{1}{x^5}=?$

• A. $723$
• B. $724$
• C. $725$
• D. $726$

Answer 1

Answer: (B)

$724$

Given,

$x+\frac{1}{x}=4$......(1).

Now squaring both sides we get,

$x^2+2+\frac{1}{x^2}=16$

or, $x^2+\frac{1}{x^2}=14$.......(2).

Now again cubing equation (1) we get,

$x^3+3.x.\frac{1}{x}(x+\frac{1}{x})+\frac{1}{x^3}=64$

or, $x^3+\frac{1}{x^3}=64-12$

or, $x^3+\frac{1}{x^3}=52$.......(3).

Now multiplying (2) and (3) we get,

$x^5+x+\frac{1}{x}+\frac{1}{x^5}=728$

or, $x^5+\frac{1}{x^5}=728-4=724$. [ Using (1)].