Question

If x+1/x = root 7 find the value the value of x^4+1/x^4

Answer 1

$\huge\underline{ \underline{ \mathfrak{answer}}}$

According to the question...

$given = x + \frac{1}{x} = \sqrt{7}$

$to \: find = {x}^{4} + \frac{1}{ {x}^{4} }$

From given equation we will square both side.....

${(x + \frac{1}{x} )}^{2} = { (\sqrt{7}) }^{2}$

${x}^{2} + { (\frac{1}{x}) }^{2} + 2 \times x \times \frac{1}{x} = 7$

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 7$

${x}^{2} + \frac{1}{ {x}^{2} } = 7 - 2 = 5$

${x}^{2} + \frac{1}{ {x}^{2} } = 5.......(i)$

Now squaring first equation we get,

${ (({x}^{2}) + (\frac{1}{ {x}^{2}})) }^{2} = ({5})^{2}$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 25$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 = 25$

${x}^{4} + \frac{1}{ {x}^{4} } = 25 - 2$

${x}^{4} + \frac{1}{ {x}^{4} } = 23$

..... Hence found....

Answer 2

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