Question

if x-1/x=8 find x3-1/x3​

Answer 1

See the answer below

Hope this will help you

Answer 2

The value of $\bf {x}^{3} - \frac{1}{ {x}^{3} } =536$, if $x - \frac{1}{x} = 8$

Given:

• $x - \frac{1}{x} = 8$

To find:

• Find the value of ${x}^{3} - \frac{1}{ {x}^{3} }$

Solution:

Concept/identity to be used:

• $\bf ( {a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)$
• Take cube both sides of given equation.

Step 1:

Take the given equation and cube both sides.

$\left( {x - \frac{1}{x} } \right)^{3} = ( {8)}^{3}$

or

$\left( {x - \frac{1}{x} } \right)^{3} = 512$

Step 2:

Open identity in the left hand side of equation.

${x}^{3} - \frac{1}{ {x}^{3} } - 3x \times \frac{1}{x} \left(x - \frac{1}{x} \right) =512$

or

${x}^{3} - \frac{1}{ {x}^{3} } - 3 \cancel x \times \frac{1}{\cancel x} \left(8 \right) =512$

or

${x}^{3} - \frac{1}{ {x}^{3} } - 24=512$

or

${x}^{3} - \frac{1}{ {x}^{3} } =512 + 24$

or

$\bf {x}^{3} - \frac{1}{ {x}^{3} } = 536$

Thus,

Value of ${x}^{3} - \frac{1}{ {x}^{3} }$ is 536.

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