The value of x in the equation $(x^{2} + 2)^{2} + 8 x^{2} = 6 x (x^{2} + 2)$ is equal to

2 \pm \sqrt{2}

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2 \pm \sqrt{3}

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2 \pm \sqrt{7}

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2 \pm \sqrt{10}

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Solution

The correct option is A $2 \pm \sqrt{2}$
Given,

${(x^{2} + 2)}^{2} + 8 x^{2} = 6 x (x^{2} + 2)$

divide by $x^{2}$ on both sides,

${(\frac{x^{2} + 2}{x})}^{2} + 8 = 6 (\frac{x^{2} + 2}{x})$

Let $k = \frac{x^{2} + 2}{x}$

$∴ k^{2} - 6 k + 8 = 0$

solving the above equation, we get,

$k = 4, 2$

$4 = \frac{x^{2} + 2}{x}, 2 = \frac{x^{2} + 2}{x}$

solving the above equation, we get,

$x = 2 \pm \sqrt{2}, 1 \pm i$

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