### Question 1

SSC-CGL 2020 Mar 3 Shift 2

If x² - 3x + 1 = 0, then x^6 + 1/x^6 = ?

### Solution in Detail

Given $\displaystyle x^2 - 3x + 1 = 0$

Divide both sides by $\displaystyle x$

$\displaystyle \therefore x - 3 + \frac 1x = 0$

$\displaystyle \implies x + \frac 1x = 3$

Remember: if form is x + 1/x, then cube of the power on LHS = Cube of the value on the right minus 3 times.$\displaystyle \therefore x^3 + \frac{1}{x^3} = 3^3 - 3 \times 3 $

$\displaystyle \therefore x^3 + \frac{1}{x^3} = 18$

A shortcut trick: if form is x + 1/x, square of the power on LHS = square of the value on the right minus 2.$\displaystyle \therefore x^6 + \frac{1}{x^6} = 18^2 - 2$

$\displaystyle \therefore x^6 + \frac{1}{x^6} = 322\:\underline{Ans}$

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