Question

X+1/x=4.findx^4+1/x^4​

Answer 1

Heya friend,

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

Squaring both sides,

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

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

$x^{2} + \frac{1}{x^{2} }$ = 14 ------------------------------- ( 1 )

We can see from the question, that we need

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

So, for that,

We will square both sides of equation 1 to get :-

$(x^{2} + \frac{1}{x^{2} }) ^2 = 14^{2}$

$(x^{2} )^{2} + (\frac{1}{x^{2} } )^{2} + 2(x^{2} )(\frac{1}{x^{2} } ) = 196$

$x^{4} + \frac{1}{x^{4} }$ + 2 = 196

$x^{4} + \frac{1}{x^{4} }$       = 196 - 2

           = 194

Thanks !

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