Question

x²+1/x²=51find the value of x-1/x

Answer 1

See below for your answer

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 51 \: \: \: \: \: \: \: (given) \\ \\ finding \: \: value \: \: of \: x - \frac{1}{x} \\ \\ \\ {(x - \frac{1}{x} )}^{2} = {x}^{2} - 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ (put \: \: the \: \: value \: \: of \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 51) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 51 - 2 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 49 \\ \\ \\ hence \: ( {x - \frac{1}{x} ) }^{2} = 49 \\ \\ (x - \frac{1}{x}) = \sqrt{49} \\ \\( x - \frac{1}{x}) = 7$