The solution of the equation $7^{1 + x} + 7^{1 - x} = 50$ is

0

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2

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\pm 1

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None of these

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Solution

The correct option is D $\pm 1$
$7^{1 + x} + 7^{1 - x} = 50$ can be written as
${7.7}^{x} + \frac{7}{7^{x}} = 50$
Let $7^{x}$ be t
$7 t^{2} - 50 t + 7 = 0$
$(t - 7) (7 t - 1) = 0$
$∴ t = 7, \frac{1}{7}$
$7^{x} = 7, \frac{1}{7}$
$x = - 1, 1$

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