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