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Solution set of the equation $3^{2 x^{2}} - {2.3}^{x^{2} + x + 6} + 3^{2 (x + 6)} = 0$ is

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${- 2, 3}$

${- 3, 2}$

${6, - 1}$

${1, - 6}$

answer is C.

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Detailed Solution

$3^{2 x^{2}} - {2.3}^{x^{2} + x + 6} + 3^{2 (x + 6)} = 0 \Rightarrow {(3^{x^{2}} - 3^{x + 6})}^{2} = 0 ∴ 3^{x^{2}} = 3^{x + 6} \Rightarrow x^{2} = x + 6 \Rightarrow x^{2} - x - 6 = 0 \Rightarrow x = 3 o r - 2.$

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