Question

find (x+1/x)=8, find the value of (x²+1/x²) and (x4+1/x4)?
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Answer 1

Answer:

Hence the answer is

${x}^{2} + \frac{1}{ {x}^{2} } = 62$

${x}^{4} + \frac{1}{ {x}^{4} } = 3842$

Step-by-step explanation:

$x + \frac{1}{x} = 8 \\ taking \: square \: on \: both \: side \\( {x + \frac{1}{x} })^{2} = ( {8})^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 64 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 64 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 64 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 62$

${x}^{4} + \frac{1}{ {x}^{4} } = ( {x}^{2} + \frac{1}{ {x}^{2} } ) ^{2} - 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } \\ {x}^{4} + \frac{1}{ {x}^{4} } = ({62})^{2} - 2 \\ = 3844 - 2 \\ = 3842$