Question

if (x-2/x)=6 , find the value of x3-8/x3 ​

Answer 1

$x - \frac{2}{x} = 6 \\ sqare \: both \: sides \: \\ (x - \frac{2}{x}) ^{2} = {6}^{2} \\ {x}^{2} + \frac{4}{ {x}^{2} } - 4 = 36 \\{x}^{2} + \frac{4}{ {x}^{2} } = 36 + 4 = 40$

Now we have to find value of :

${x}^{3} - \frac{8}{ {x}^{3} }$

Solution :

$( {x})^{3} - (\frac{2}{x} )^{3}$

Using identity : a³-b³ = (a - b)(a² + b² +ab)

$= (x - \frac{2}{x} )( {x}^{2} + \frac{4}{ {x}^{2} } + 2)$

Now put the values that we have calculated above :

= (6)(40 + 2)

= (6)(42)

= 252

ANSWER : 252

HOPE IT HELPS !!

MARK BRAINLIEST !!

Answer 2

EXPLANATION.

⇒ (x - 2/x) = 6.

As we know that,

Cubing on both sides of the equation, we get.

⇒ (x - 2/x)³ = (6)³.

⇒ (x)³ - 3(x)²(2/x) + 3(x)(2/x)² - (2/x)³ = (6)³.

⇒ x³ - (6x) + (12/x) - (8/x³) = 216.

⇒ x³ - 6(x - 2/x) - 8/x³ = 216.

Put the value of (x - 2/x) = 6 in the equation, we get.

⇒ x³ - 6(6) - 8/x³ = 216.

⇒ x³ - 36 - 8/x³ = 216.

⇒ x³ - 8/x³ = 216 + 36.

⇒ x³ - 8/x³ = 252.