Question 137

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

Solution

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

squaring both sides

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

$$x^{2}+\frac{1}{x^2}$$ = 16-2 = 14

again squaring both sides

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

$$x^{4}+\frac{1}{x^4}$$ = 196 - 2 = 194

Create a FREE account and get: