Question

If x²+1/x²=51 then find x+1/x​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 51$

${x}^{2} + \frac{1}{ {x}^{2} } =49 + 2$

${x}^{2} + \frac{1}{ {x}^{2} } - 2 = 49$

${x}^{2} + \frac{1}{ {x}^{2} } - 2( {x}^{2})( \frac{1}{ {x}^{2} } ) = 49$

$(x + \frac{1}{x} ) {}^{2} = 49$

$x + \frac{1}{x} = \sqrt{49}$

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

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