Question

X-1/x=4 then evaluate x2+1/x2 and x4+1/x4

Answer 1

Answer:

$x - \frac{1}{x} = 4$

${ (x - \frac{1}{x}) }^{2} = {4}^{2}$

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

${x}^{2} + \frac{1}{ {x}^{2} } = 16 + 2 = 18$

${ ({x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {18}^{2}$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 = 324$

${x}^{4} + \frac{1}{ {x}^{4} } = 324 - 2 = 322$