Question

If $x+\frac{1}{x}=3$, then $x^4+\frac{1}{x^4}$=

• A. $81$
• B. $23$
• C. $25$
• D. $47$

Answer 1

Answer: (D)

$47$

$x+\frac{1}{x}=3$

Squaring both sides

$\Rightarrow x^2+\frac{1}{x^2}+2=9$ ........ $(a+b{)}^2=a^2+2ab+b^2$

$\Rightarrow x^2+\frac{1}{x^2}=7$

Again, Squaring both sides

$\Rightarrow {\left(x^2+\frac{1}{x^2}\right)}^2=49$

$\Rightarrow x^4+\frac{1}{x^4}+2=49$ ......$(a+b{)}^2=a^2+2ab+b^2$

$\Rightarrow x^4+\frac{1}{x^4}=47$