Question

If $x^4+\frac{1}{x^4}=623,\text{then}x+\frac{1}{x}=$

• A. 27
• B. 25
• C. $3\sqrt{3}$
• D. $-3\sqrt{3}$

Answer 1

The correct option is C

$3\sqrt{3}$

$x^4+\frac{1}{x^4}=623\text{Adding 2 to both sides},x^4+\frac{1}{x^4}+2=623+2=625{(x^2+\frac{1}{x^2})}^2=(25{)}^2\therefore x^2+\frac{1}{x^2}=25\text{Adding 2 to both sides,}{x}^2+\frac{1}{x^2}+2=25+2=27{(x+\frac{1}{x})}^2=(\sqrt{2}7{)}^2={\left[\sqrt{9\times 3}\right]}^2\therefore x+\frac{1}{x}=3\sqrt{3}$