Solve for x:

$3^{x^{2}} : 3^{x} = 9 : 1$ ,
Enter only positive value

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Solution

The correct option is A 2
$3^{x^{2}} : 3^{x} = 9 : 1$
$=> \frac{3^{x^{2}}}{3^{x}} = \frac{3^{2}}{1}$
$=> 3^{x^{2} - x} = 3^{2}$
$=> x^{2} - x = 2$
$=> x^{2} - x - 2 = 0$
$=> x^{2} - 2 x + x - 2 = 0$
$=> x (x - 2) + (x - 2) = 0$
$=> () x - 2) (x + 1) = 0$
$=> x = 2$ or $x = - 1$

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