Question

$find \: {x}^{3} + \frac{1}{ {x}^{3} }$
if
$x + \frac{1}{x} = 3$
​

Answer 1

Answer:

see below

Step-by-step explanation:

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Answer 2

Answer:

The value of x³ + ( 1 / x³ ) is 18.

Step-by-step-explanation:

We have given that,

x + ( 1 / x ) = 3

We have to find the value of x³ + ( 1 / x³ ).

Now,

x + ( 1 / x ) = 3

Taking cube on both sides, we get,

⇒ x³ + 3 * x² * ( 1 / x ) + 3 * x * ( 1 / x )² + ( 1 / x )³ = 3³

⇒ x³ + ( 1 / x³ ) + 3 * x * x ÷ x + 3 * x * 1 / x² = 27

⇒ x³ + ( 1 / x³ ) + 3x + 3x / x = 27

⇒ x³ + ( 1 / x³ ) + 3 [ x + ( 1 / x ) ] = 27

⇒ x³ + ( 1 / x³ ) + 3 * 3 = 27

⇒ x³ + ( 1 / x³ ) + 9 = 27

⇒ x³ + ( 1 / x³ ) = 27 - 9

⇒ x³ + ( 1 / x³ ) = 18

∴ The value of x³ + ( 1 / x³ ) is 18.