Question

x- 1/x=3 then x^3- 1/x^3=?​

Answer 1

EXPLANATION.

⇒ (x - 1/x) = 3.

As we know that,

Cube on both sides of the equation, we get.

⇒ (x - 1/x)³ = (3)³.

⇒ x³ - 3(x)²(1/x) + 3(x)(1/x)² - (1/x)³ = 27.

⇒ x³ - 3x + 3/x - 1/x³ = 27.

⇒ x³ - 1/x³ - 3x + 3/x = 27.

⇒ x³ - 1/x³ - 3(x - 1/x) = 27.

Put the value of (x - 1/x) = 3 in the equation, we get.

⇒ x³ - 1/x³ - 3(3) = 27.

⇒ x³ - 1/x³ - 9 = 27.

⇒ x³ - 1/x³ = 27 + 9.

⇒ x³ - 1/x³ = 36.

Answer 2

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$\mapsto$ $(x-\frac{1}{x}) = 3$

We know that,

• $\leadsto$ Cube on both sides of the equation, we get;

$\implies$ (x - 1/x)³ = (3)³

$\implies$ x³ - 3(x)²(1/x) + 3(x)(1/x)² - (1/x)³ = 27

$\implies$ x³ - 3x + 3/x - 1/x³ = 27

$\implies$ x³ - 1/x³ - 3x + 3/x = 27

$\implies$x³ - 1/x³ - 3(x - 1/x) = 27

• $\leadsto$ Put the value of (x - 1/x) = 3 in the equation, we get;

$\implies$ x³ - 1/x³ - 3(3) = 27

$\implies$ x³ - 1/x³ - 9 = 27

$\implies$ x³ - 1/x³ = 27 + 9

$\implies$ x³ - 1/x³ = 36