Question 70

If $$\left(x - \frac{1}{x}\right)^2 = 3$$, then the value of $$x^6 + \frac{1}{x^6}$$ equals

Solution

$$\left(x - \frac{1}{x}\right)^2 = 3$$

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

$$x^2 + \frac{1}{x^2}= 5 $$ { $$ x+\frac{1}{x} = k then x^3 +\frac{1}{x^3} = k^3-3k$$}

$$ x^6 + \frac{1}{x^6} = 5^3 - 3 \times 5$$ = 125 -15 = 110

$$ x^6 + \frac{1}{x^6} = 110$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: