Question

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

• A. 196
• B. 194
• C. 192
• D. 190

Answer 1

The correct option is B

194

$x+\frac{1}{x}=4\text{Squaring, we get}{x}^2+\frac{1}{x^2}+2=16\Rightarrow x^2+\frac{1}{x^2}=16-2=14\text{Again squaring,}{x}^4+\frac{1}{x^4}+2=196\Rightarrow x^4+\frac{1}{x^4}=196-2=194$