If {x-(1/x)} = 11, what is the value of [x^4+{1/(x^4)}]?

Question : If $x-\cfrac{1}{x} = 11$, what is the value of $(x^4+\cfrac{1}{x^4})$ ?

14159

14163

15127

15131

Solution: $\require{cancel}$

$x-\frac{1}{x} = 11$
or, $ (x-\frac{1}{x})^2 = (11)^2 $
or, $ x^2 + \frac{1}{x^2} - 2\times \cancel{x} \times \frac{1}{\cancel{x}} = 121 $
or, $(x^2 + \frac{1}{x^2})^2 = (121+2)^2 $
or, $x^4+\frac{1}{x^4} +2 \times \cancel{x^2} \times \frac{1}{\cancel{x^2}} = (123)^2 $
or, $x^4+\frac{1}{x^4} = 15129 - 2 $
or, $x^4+\frac{1}{x^4} = 15127 $

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