If (x² - 1/(x²)=4√(6)), , and x > 1what is the value of (x³ - 1/(x³))?

If (x² - 1/(x²)=4√(6)), , and x > 1what is the value of…

If $(x^2 - \frac{1}{x^2}=4\sqrt{6}),$ , and x > 1what 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. 22 $\sqrt{2}$ .

x² - 1/x² = $4\sqrt6$

⇒ x⁴+ 1/x⁴- 2 = 96

x⁴+ 1/x⁴ = 98

⇒ x² + 1/x² = $\sqrt{(98+2)}$ = 10

⇒ x + 1/x = $\sqrt{(10+2)}$ = $\sqrt{12}$

⇒ x - 1/x = $\sqrt{(\sqrt{12})^2 - 4}$

⇒ x - 1/x = 2 $\sqrt2$

⇒ x³ - 1/x³ = 16 $\sqrt2$ + 6 $\sqrt2$ = 22 $\sqrt2$