Question

If x - 1/x =√5 , find the value of x³ +1/x³​

Answer 1

The value of $x^{3}-\frac{1}{x^{3}}$ is 2√5.

Step-by-step explanation:

The expansion of (a - b)³ is:

(a - b)³ = a³ - b³ - 3ab (a - b)

It is provided that:

$x-\frac{1}{x}=\sqrt{5}$

Compute the value of $x^{3}-\frac{1}{x^{3}}$ as follows:

$(x-\frac{1}{x})^{3}=(\sqrt{5})^{3}$

$x^{3}-\frac{1}{x^{3}}-[3\times x\times \frac{1}{x}(x-\frac{1}{x})]=(\sqrt{5})^{3}$

$x^{3}-\frac{1}{x^{3}}-[3(x-\frac{1}{x})]=(\sqrt{5})^{3}$

$x^{3}-\frac{1}{x^{3}}-3\sqrt{5}=(\sqrt{5})^{3}$

$x^{3}-\frac{1}{x^{3}}=(\sqrt{5})^{3}-3\sqrt{5}$

$x^{3}-\frac{1}{x^{3}}=\sqrt{5}[(\sqrt{5})^{2}-3]$

$x^{3}-\frac{1}{x^{3}}=2\sqrt{5}$

Thus, the value of $x^{3}-\frac{1}{x^{3}}$ is 2√5.

Learn more:

https://brainly.in/question/1712869