Question

$\Large\mathfrak\red{hey! \: guys}$

$\huge\mathfb\red{please\:solve\:these\: problem}$

$\tt\implies$

$\sf{\blue{\purple{\bigstar{\mathbf{\red{find\:the value of given eq}}}}}}$
$\sf\underline\bold{1)}$ $\sf if X + \dfrac{1}{x} =3$

$\sf\mathfb\red{then,\:find\:the\:value\:of,}$

$\large\implies X^3 + \frac{1}{x^3}$

$\rule{300}3$

instructions:-
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$<marquee scrollamount=600>SanTaBeaTs✌️$
​

Answer 1

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$\Huge{\underline{\underline{\sf{Given}}}} \ :$

• $\:\:\Large\sf{x \ + \ \dfrac{1}{x} \ = \ 1}$

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$\Huge{\underline{\underline{\sf{To\:Find }}}} \: :$

• $\:\:\Large\sf{Value \ of \ x^3 \ + \ \dfrac{1}{x^3} }$

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$\Huge{\underline{\underline{\sf{Solution }}}} \::$

$\dashrightarrow\:\:\sf{x \ + \ \dfrac{1}{x} \ = \ 3}$

$\sf{Cubing \ on \ both \ sides \ :}$

$\dashrightarrow\:\:\sf{\bigg( x \ + \ \dfrac{1}{x} \bigg)^3 \ = \ ( 3 )^3}$

$\sf{\bigg[Using \ identity \ : \ (a \ - \ b)^3 \ = \ a^3 \ - \ b^3 \ - \ 3ab \ (a \ - \ b)\bigg]}$

$\dashrightarrow\:\:\sf{ x^3 \ - \ \dfrac{1}{x^3} \ - \ 3 \ \bigg( x \ - \ \dfrac{1}{x} \bigg) \ = \ 27}$

$\dashrightarrow\:\:\sf{ x^3 \ - \ \dfrac{1}{x^3} \ - \ 3 ( 3 ) \ = \ 27}$

$\dashrightarrow\:\:\sf{ x^3 \ - \ \dfrac{1}{x^3} \ - \ 9 \ = \ 27}$

$\dashrightarrow\:\:\sf{ x^3 \ - \ \dfrac{1}{x^3} \ = \ 27 \ + \ 9}$

$\dashrightarrow\:\:{\boxed{\sf{\:\: x^3 \ - \ \dfrac{1}{x^3} \ = \ 36\:\:}}}$

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