If $x+\frac{1}{x}=4$, then the value of $x^4 +(\frac{1}{x})^4$ is :
Answer & explanation
Correct answer: option 4
$(x - \frac{1}{x}) = a$
(x2 + x-2) = (a)2 + 2 = b
= (x4 + x-4) = b2 - 2
If $x+\frac{1}{x}=4$,
(x2 + x-2) = (4)2 - 2 = 14
then the value of $x^4 +(\frac{1}{x})^4$ is = (14)2 - 2 = 194