Question

If $x=3+\sqrt{8}$ find the value of $x^4+\frac{1}{x^4}$

• A. 1254
• B. 1064
• C. 1154
• D. 1206

Answer 1

Answer: (C)

1154

$x+\frac{1}{x}=6$
$\therefore x^2+\frac{1}{x^2}={(x+\frac{1}{x})}^2-2=36-2=34$
$\Rightarrow x^4+\frac{1}{x^4}={(x^2+\frac{1}{x^2})}^2-2$
$={34}^2-2=1154$