Question

If, $(x+\frac{1}{x})=4$, then the value of $x^4+\frac{1}{x^4}$ is:

• A. 64
• B. 194
• C. 81
• D. 124

Answer 1

Answer:

B. 194

Solution:

Given:

$(x+\frac{1}{x})=4$,

Formula used:

(a + b)² = a² + b² + 2ab

Calculations:

According to the question, we have

Squaring both sides,

$x^2+\frac{1}{x^2}+2=16$

$x^2+\frac{1}{x^2}=14$

Squaring both sides again, we get

$x^4+\frac{1}{x^4}+2=196$

$x^4+\frac{1}{x^4}=196-2$

∴ The value of $x^4+\frac{1}{x^4}$  is 194.