If x² + 1/(x²) = 18, x > 0, then find the vale of x³ + 1/(x³) .

If x² + 1/(x²) = 18, x > 0, then find the vale of x³ +…

If x² + $\frac{1}{x^2}$ = 18, x > 0, then find the vale of x³ + $\frac{1}{x^3}$ .

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 34 $\sqrt{5}$

(a + b)² = a² + b² + 2ab ---- (1)

(a + b)³ = a³ + b³ + 3ab(a + b) ----- (2)

Using equation (1), we get

⇒ (x + 1/x)² = x² + 1/x² + 2

⇒ (x + 1/x)² = 18 + 2 = 20

⇒ (x + 1/x) = $2\sqrt5$

Using equation (2), we get

⇒ (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

⇒ 40√5 = x³ + 1/x³ + 6√5

⇒ x³ + 1/x³ = 34√5