Question

evaluate x³-1/x³ if x-1/x=6​

Answer 1

EXPLANATION.

⇒ x - 1/x = 6.

As  we know that,

Cubing on both sides of the equation, we get.

⇒ (x - 1/x)³ = (6)³.

⇒ x³ - 3(x)²(1/x) + 3(x)(1/x)² - (1/x)³ = 216.

⇒ x³ - 3x + 3/x - 1/x³ = 216.

⇒ x³ - 3(x - 1/x) - 1/x³ = 216.

Put the value of x - 1/x = 6 in the equation, we get.

⇒ x³ - 3(6) - 1/x³ = 216.

⇒ x³ - 18 - 1/x³ = 216.

⇒ x³ - 1/x³ = 216 + 18.

⇒ x³ - 1/x³ = 234.

Answer 2

$\huge \boxed { \sf \blue{ {x}^{3} - \frac{1}{ {x}^{3} } = 234}}$

Step-by-step explanation:

Q.

$\sf \: evaluate : {x}^{3} - \frac{1}{ {x}^{3} } \\ \sf \: if \: x - \frac{1}{x} = 6$

Solution -

$\sf \: x - \frac{1}{x} = 6 \\ \\ \sf= > {(x - \frac{1}{x}) }^{3} = {6}^{3} ....(cubing \: both \: sides) \\ \\ \sf = > {x}^{3} - ( { \frac{1}{x}) }^{3} - 3( \cancel{x \: }) (\frac{1}{ \cancel{x \: }} )(x - \frac{1}{ x} ) = 216 \\ \\ \{ \sf \: by \: the \: formula \: ( {a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \} \\ \\ \sf = > {x}^{3} - \frac{1}{x {}^{3} } - 3(6) = 216 \\ \\ \sf = > {x}^{3} - \frac{1}{ {x}^{3} } - 18 = 216 \\ \\ \sf = > {x}^{3} - \frac{1}{ {x}^{3} } = 216 + 18 \\ \\ = > \sf \underline{ {x}^{3} - \frac{1}{ {x}^{3} } = 234}$

hope it helps.