Question

If x+1/x =11 then find the value of x-1/x​

Answer 1

Answer:

x - 1/x = under root 117

Step-by-step explanation:

x + 1/x = 11

Squaring both the sides

we get,

x^2 + 1/x^2 + 2 = 121

x^2 + 1/x^2 = 119

We have to find x -1/x

(x - 1/x)^2 = x^2 + 1/x^2 - 2

x - 1/x = under root 119 - 2

x - 1/x = under root 117

Answer 2

Answer:

$\sqrt{117}$

Step-by-step explanation:

$x + \frac{1}{x} = 11 \: on \: squaring \: both \: sides \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 121 \\ from \: here \: we \: get \: {x}^{2} + \frac{1}{ {x}^{2} } = 119 \\ now \: \:let \: equation \: x - \frac{1}{x} = y \\ on \: squaring \: both \: sides \: we \: get \: {x}^{2} + \frac{1}{ {x}^{2} } - 2 = {y}^{2} \\ putting \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } \: from \: above \: we \: get \: {y}^{2} = 117 \\ now \: y = \sqrt{117}$