Question

If the value of,x-1/x=4 then prove that x^4 +1/x^4 = 322

Answer 1

$\bold{ \huge{ Answer:-} }\\x-\frac{1}{x}=4\\Squaring \: on \: both \: the \: sides \\ {(x-\frac{1}{x})}^{2}={(4)}^{2}\\{(x)}^{2}+{(\frac{1}{x})}^{2}-2(x)(\frac{1}{x})={(4)}^{2}\\{x}^{2}+\frac{1}{x^{2}}-2=16\\{x}^{2}+\frac{1}{x^{2}}=16+2\\{x}^{2}+\frac{1}{x^{2}}=18\\Squaring \: on \: both \: the \: sides \\{( {x}^{2} + \frac{1}{ {x}^{2} })}^{2}={(18)}^{2}\\{( {x}^{2} )}^{2}+{(\frac{1}{ {x}^{2} })}^{2} + 2( {x}^{2} )(\frac{1}{ {x}^{2} })={(18)}^{2}\\{x}^{4}+\frac{1}{x^{4}} + 2=324\\{x}^{4}+\frac{1}{x^{4}}=324 - 2\\{x}^{4}+\frac{1}{x^{4}}=322 \\ Hence \: proved$