Question

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x=4​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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$\Longrightarrow \bigg(x + \frac{1}{x} \bigg) = 4$

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BY SQUARING BOTH SIDE WE GET:---

$\Longrightarrow \bigg(x + \frac{1}{x} \bigg) {}^{2} = 16$

$\Longrightarrow \: x {}^{2} + \frac{1}{x {}^{2} } + 2 \times { \cancel{x}} \times \frac{1} {\cancel{x}} = 16$

$\Longrightarrow x {}^{2} + \frac{1}{x {}^{2} } = 14$

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BY SQUARING IT BOTH SIDE AGAIN WE GET:--

$\Longrightarrow \bigg(x {}^{2} + \frac{1}{x {}^{2} } \bigg) {}^{2} = 14 {}^{2}$

$\Longrightarrow \: x {}^{4} + \frac{1}{x {}^{4} } + 2 \times \cancel x {}^{2} \times \frac{1} {\cancel {x {}^{2} } } = 196$

$\Longrightarrow \: x {}^{4} + \frac{1}{x {}^{4} } = 194$