If , (x² + 1/(x²)) = 18 and x > 0, what is the value of (x³ + 1/(x³))?

If , (x² + 1/(x²)) = 18 and x > 0, what is the value of…

If , $(x^2 + \frac{1}{x^2}) = 18$ and x > 0, what is the value of $(x^3 + \frac{1}{x^3})?$

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 34 $\sqrt{5}$

Given that

$(x^2 + \frac{1}{x^2}) = 18$

Adding 2 to both sides we get

( $x+\frac{1}{x}$ )² = 20

⇒ $x+\frac{1}{x}$ = √20

Cubing both sides we get

( $x+\frac{1}{x}$ )³ = (√20)³

⇒ x³ + ( $\frac{1}{x}$ )³ + 3( $x+\frac{1}{x}$ ) = 20√20

⇒ $(x^3 + \frac{1}{x^3})$ = 20√20 - 3√20 = 17√20 = 34√5.