Question

x+1/X =5 find x³+1/x³
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Answer 1

Given:

• ${\small{\bold{\dfrac{x+1}{x} = 5}}}$

To Find:

• ${\small{\bold{\dfrac{x^3 + 1}{x ^{3} } }}}$

Solution:

${\small{\tt{\dfrac{x+1}{x} = 5}}}$

${\small{\tt{\implies{\dfrac{x}{x} + \dfrac{1}{x} = 5}}}}$

${\small{\tt{\implies{ 1 + \dfrac{1}{x} = 5}}}}$

${\small{\tt{\implies{\dfrac{1}{x} = 5-1 }}}}$

${\small{\tt{\implies{\dfrac{1}{x} = 4}}}}$

${\small{\tt{\implies{x = \dfrac{1}{4}}}}}$

Now,

${\small{\tt{\dfrac{x^3 + 1}{x^3} }}}$

${\small{\tt{ = \dfrac{x^3}{x^3} + \dfrac{1}{x^3} }}}$

${\small{\tt{=1 + \dfrac{1}{x^3}}}}$

${\small{\bold{Put \ x = \dfrac{1}{4}}}}$

${\small{\tt{= 1 + \dfrac{1}{ \bigg(\dfrac{1}{4} \bigg)^3}}}}$

${\small{\tt{ = 1 + 4^3}}}$

${\small{\tt{ = 1 + 64}}}$

${\small{\bold{\underline{\boxed{ = {64}}}}}}$

$\begin{array}{c}{\large{\frak{\red{Which \ is \ the \ required }}}} \\ {\large{\frak{\red{Answer }}}} \end{array}$