Question

If x - 1/x = 7, then what is the value of x³ - 1/x³

Answer 1

Answer:

⇒ $x^3 - \frac{1}{x^3} = 364$

Step-by-step explanation:

Given :

To find the value of $x^3 - \frac{1}{x^3}$ if,

⇒ $x - \frac{1}{x} = 7$

Solution :

We know that,

$(a - b)^3 = a^3 - b^3 - 3ab(a-b)$

⇒ $x - \frac{1}{x} = 7$

⇒ $(x - \frac{1}{x})^3 = 7^3$

⇒ $x^3 - \frac{1}{x^3} - 3(x)(\frac{1}{x})(x - \frac{1}{x}) = 343$

⇒ $x^3 - \frac{1}{x^3} - 3(1)(7) = 343$

⇒ $x^3 - \frac{1}{x^3} - 21 = 343$

⇒ $x^3 -\frac{1}{x^3}= 343+21 = 364$

Answer 2

I Hope my answer helps you..