Question

if x-1/X = 8 then the value of x"4+/1X"4
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Answer 1

Given: $\:\sf x - \frac{1}{x} = 8$

squaring on both sides

$\sf {(x - \frac{1}{x} )}^{2} = {8}^{2}$

$\sf {{x}^{2} + \frac{1}{{x}^{2} } - 2= 64}$

$\sf {{x}^{2} + \frac{1}{{x}^{2} } = 64 + 2}$

$\sf {{x}^{2} + \frac{1}{{x}^{2} } = 66}$

now again squaring on both sides

$\sf {({{x}^{2} + \frac{1}{{x}^{2} } ) }^{2} = {66}^{2} }$

$\sf {{{x}^{4} + \frac{1}{{x}^{4} } + 2} = 4356 }$

$\fbox{\sf {{{x}^{4} + \frac{1}{{x}^{4} } } = 4354 }}$