Question

If x^2+1/x^2=38. Find the value of.. x-1/x

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 38 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 38 - 2 \\ {(x - \frac{1}{x} )}^{2} = 36 \\ x - \frac{1}{x} = 6$

Answer 2

$\mathfrak{ \fcolorbox {blue}{white} { \red{Solution:- } } }$

$\red{ = > }\huge{{x}^{2} + \frac{ 1}{ {x}^{2} } = 38 } \\ \\ \huge \mathfrak{ \red{substract \: 2 \: on \: both \: sides.} } \\ \\ \red{ = > }\huge{ {x}^{2} + \frac{ 1 }{ {x}^{2} } - 2 } = 38 - 2 \\ \\ \red{ = > }\huge{ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 36} \\ \\ \huge \mathfrak{ \red{we \: can \: wrte \: it \: as\: }} \\ \\ \red{ = > }\huge{ {x}^{2} - 2 + \frac{1}{ {x}^{2} } = 36 } \\ \\ \mathfrak{\red{ we \: know \: { ({a - b})^{2} } } = {a}^{2} - 2ab + {b}^{2} } \\ \\ \mathfrak \red{ \huge{now}} \\ \\ \red{ = > }\huge{ ( {x - \frac{1}{x} })^{2} } = 36 \\ \\ \red{ = > }\huge{ x - \frac{1}{x} } = \sqrt{36} \\ \\ \red{ = > }\huge{x - \frac{1}{x} = 6 } \\ \\ \fcolorbox{blue} {white}{i \: hope \: it \: helps \: you.}$