Question

if
$a - \frac{1}{a} = 3 \: \: \: then \: \: \: {a}^{3} - \frac{1}{ {a}^{3} } =$

Answer 1

Hey friend, Harish here.

Here is your answer:

Given that,

$(a- \frac{1}{a}) = 3$

To find,

$(a^{3}- \frac{1}{a^{3}}) 's\ Value$

Solution:

We know that,

( x - y )³ = x³ - y³ - 3xy (x - y)

Then,

$(a- \frac{1}{a})^{3}=a^{3} - \frac{1}{a^{3}} - 3(a)( \frac{1}{a}) ( a - \frac{1}{a})$

Here a & 1/a will get canceled. 

⇒ $3^{3} = a^{3} - \frac{1}{a^{3}}- 3(a- \frac{1}{a})$ 

⇒ $27 = a^{3} - \frac{1}{a^{3}}- 3(3)$

⇒  $a^{3} - \frac{1}{a^{3}} = 27 - 9 = 18$

Therefore the answer is 18.
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Hope my answer is helpful to you.