Question

if x^2 + 1 / x^2 = 83 . find the value of x^3 - 1/ x^3

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Answer 1

Answer:

56 is the correct answer

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Answer 2

Answer:

→ Hey Mate,

→ Given Question : if    $x^{2} + \frac{1}{x^2} = 83 .$  find the value of  $x^{3} - \frac{1}{x^3}$

→ Step-by-step explanation:

→ Solution :

→ $( x-\frac{1}{x} )^2 = x^2 + \frac{1}{x^2} -2$

→ $( x - \frac{1}{x} ) ^2 = 83 - 2$                           [  Putting $x^2 + \frac{1}{x^2} = 83$ ]

→ $( x - \frac{1}{x^2} ) = 81$

→ $( x - \frac{1}{x^2} ) = 9^2$

→ $x - \frac{1}{x} = 9$                                         [ Taking square root of both sides]

→ $( x - \frac{1}{x} ^3 ) = 9^3$                                     [ cubing both sides]

→ $(x^3 - \frac{1}{x^3} ) - 3 ( x - \frac{1}{x} ) = 729$            

→ $x^3 - \frac{1}{x^3} - 3$ ×  $9 = 279$

⇒ $x^3 - \frac{1}{x^3} = 729 + 27 = x^3 - \frac{1}{x^3} = 756$

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