The values of $x$ satisfying $x^{2 / 3} + 12 = 7 x^{1 / 13}$ are

3, 4

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3^{13}, 4^{13}

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{(\frac{4}{3})}^{13}, {(\frac{3}{4})}^{13}

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3^{1 / 13}, 4^{1 / 13}

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Solution

The correct option is C $3^{1 / 13}, 4^{1 / 13}$
$x^{2 / 13} + 2 = 7 x^{1 / 3}$
$m^{2} - 7 m + 12 = 10$ , where $m = x^{1 / 3}$
$(m - 4) (m - 3) = 0$
i.e., $m = 4$ or $m = 3$
$∴ x^{1 / 3} = 4$ or $x^{1 / 13} = 3$
i.e., $x = 4^{1 / 13}$ or $3^{1 / 13}$

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Similar questions

The possible values of expression $\frac{1}{x^{2} - x - 3}$ is

3 \frac{1}{12} - [1 \frac{3}{4} + {2 \frac{1}{2} - (1 \frac{1}{2} - \frac{1}{3})}]

3 \frac{1}{12} - [1 \frac{3}{4} + {2 \frac{1}{2} - (1 \frac{1}{2} - \frac{1}{3})}]

What is the value of:
$3 \frac{1}{12} - [1 \frac{3}{4} + {2 \frac{1}{2} - (1 \frac{1}{2} - \frac{1}{3})}]$

3 \frac{1}{12} - [1 \frac{3}{4} + {2 \frac{1}{2} - (1 \frac{1}{2} - \frac{1}{3})}]

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