Question

Is x square + 1 / x square = 27, find the value of x + 1 / x
plzzz answer me plz

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ \\ \\ adding \: \: \: 2(x \times \frac{1}{x} ) \: \: \: \: on \: \: both \: sides$


Hence,

${x}^{2} + \frac{1}{ {x}^{2} } + 2(x \times \frac{1}{x} ) = 27 + 2(x \times \frac{1}{x} )$

We know,
${x}^{2} + \frac{1}{ {x}^{2} } + 2(x \times \frac{1}{x} ) = {(x + \frac{1}{x}) }^{2}$

On Applying formula, we get


$(x + \frac{1}{x} ) ^{2} = 27 + 2 \\ \\ \\ => {(x + \frac{1}{x} )}^{2} = 29 \\ \\ \\ => x + \frac{1}{x} = \sqrt{29}$