Question

if x²+1/x² = 7 find the value of x+1/x​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ = > ( {x + \frac{1}{x} )}^{2} - 2.x. \frac{1}{x} = 7 \\ \\ = > ( {x + \frac{1}{x} )}^{2} - 2 = 7 \\ \\ = > ( {x + \frac{1}{x} )}^{2} = 7 + 2 \\ \\ = >( {x + \frac{1}{x}) }^{2} = 9 \\ \\ = > x + \frac{1}{x} = \sqrt{9} \\ \\ = > x + \frac{1}{x} = 3.$