The number of real roots of $3^{2 x^{2} - 7 x + 7} = 9$ is :

2

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1

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4

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0

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Solution

The correct option is A $2$
$3^{2 x^{2} - 7 x + 7} = 9 \Rightarrow 3^{2 x^{2} - 7 x + 7} = 3^{2}$

$\Rightarrow 2 x^{2} - 7 x + 7 = 2 \Rightarrow 2 x^{2} - 7 x + 5 = 0$

Here Discriminant $= (- 7)^{2} - 4 (2) (5) = 49 - 40 = 9 > 0$

Hence, the given equation has two real roots.

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3^{2 x^{2} - 7 x + 7} = 9

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