Question

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$a + \frac{1}{a} = 5 \: find \: {a}^{3} + \frac{1}{ {a}^{3} }$
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Answer 1

Answer:

Heya mate !! here is the answer ❤

Answer 2

$\huge\mathfrak{solution}$

Given:

$\boxed{ \bold{a + \frac{1}{a} = 5}}$

To find :

$\boxed{ \bold{{a}^{3} + \frac{1}{ {a}^{3} } }}$

$\leadsto \: a + \frac{1}{ a} = 5$

cube both sides , we get

$\leadsto \: ( {a + \frac{1}{ a} )}^{3} = {5}^{3} \\ \\ \leadsto \: {a}^{3} + \frac{1}{ {a}^{3} } + 3(a)( \frac{1}{a} )(a + \frac{1}{a} ) = 125 \\ \\ \leadsto \: {a}^{3} + \frac{1}{ {a}^{3} } + 3 \cancel{a}( \frac{1}{ \cancel{a}} )(5) = 125 \\ \\ \leadsto \: {a}^{3} + \frac{1}{ {a}^{3} } = 125 - 15 \\ \\ \leadsto \: {a}^{3} + \frac{1}{ {a}^{3} } = 110$

Formula:

$\boxed{ \bold{( {x}^{3} + {y}^{3} ) = {x}^{3} + {y}^{3} + 3xy(x + y)}}$