Question

if (x+1/x)=√5, find the value of a+1/x²andx⁴+1/X3.​

Answer 1

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Answer 2

Answer:

$Given,$

$x - \frac{1}{x} = 5$

$Squaring \: both \: the \: sides \: ,$

$(x - \frac{1}{x} ) {}^{2} = 5 {}^{2}$

$x {}^{2} + \frac{1}{x {}^{2} } - 2(x)( \frac{1}{x}) = 25$

$x {}^{2} + \frac{1}{x {}^{2} } = 25 + 2$

$x {}^{2} + \frac{1}{x {}^{2} } = 27$

$Now,$

$x {}^{3} - \frac{1}{x {}^{3} }$

$(x - \frac{1}{x} )[(x) {}^{2} + ( \frac{1}{x {}^{2} } ) + (x)( \frac{1}{x} )]$

$= 5(27 + 1)$

$= 5 \times 28$

$= 140$