Math, asked by abhinandrv, 11 months ago

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

Answers

Answered by sakshi86200511
8

Answer:

Heya mate !! here is the answer ❤

Attachments:
Answered by kaushik05
23

  \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)}}

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