Question

if x-1/x=2, find
x^4+1/x^4
Please answer.

Answer 1

see the attachment........

Answer 2

Answer:

$x^4 + \frac{1}{x^4} = 34$

Step-by-step explanation:

Given that, $x - \frac{1}{x} = 2$

$=>(x - \frac{1}{x})^2 = 2^2$  [squared both sides]

$=>x^2 - 2.x.\frac{1}{x} + \frac{1}{x^2} = 4$  [using the identity $(a - b)^2 = a^2 - 2ab + b^2$]

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

$=>x^2 + \frac{1}{x^2} = 4 + 2 = 6$

$=>(x^2 + \frac{1}{x^2})^2 = 6^2$   [squared both sides]

$=>(x^2)^2 + 2.x^2.\frac{1}{x^2} + (\frac{1}{x^2})^2 = 36$  [using the identity $(a - b)^2 = a^2 - 2ab + b^2$]

$=>x^4 + 2 + \frac{1}{x^4} = 36$  [∵ $(a^m)^n = a^{mn}$]

$=>x^4 + \frac{1}{x^4} = 36 - 2$

$=>x^4 + \frac{1}{x^4} = 34$