Question

X square + 1 / x square is equals to 51 find x

Answer 1

$Heya$‼

$Question\:Correction$:- $x^2 + ( 1/x^2) = 51$. $Find\: x^3+ 1/x^3$

$Solution$ :-

$x^2 + ( 1/x^2) = 51$

$( x + 1/x )^2 + 2 ( x ) ( 1/x ) = 51$

$( x + 1/x )^2 + 2 = 51$

$(x + 1/x )^2 = 51 - 2$

$(x + 1/x )^2 = 49$

$x + 1/x =$√49

$x + 1/x = 7$

$Now,$
$As\:we\:know,$

$a^3 - b^3$ $= (a-b)(a^2+ab+b^2)$

$So$ $x^3-1/x^3$

= (x - 1/x)(x² + x × 1/x + 1/x²)

$= (x-1/x)(x^2+1+1/x^2)$

$=7×(51+1)$

$=7 × 52$

$=364$

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