First slide

Theory of equations

Question

If $\sqrt{\sqrt{\sqrt{x}}} = \sqrt[4]{\sqrt[4]{\sqrt[4]{3 x^{4} + 4}}}$ , then the value of x⁴ it____.

Moderate

Solution

$\begin{array}{l} x^{\frac{1}{8}} = {(3 x^{4} + 4)}^{\frac{1}{64}} \\ \Rightarrow x^{8} = 3 x^{4} + 4 \\ \Rightarrow x^{4} = 4 \end{array}$

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