Question

find this this so urgent


the value of x on solving x/x-1+x-1/x=21/2 will be​

Answer 1

Step-by-step explanation:

$\frac{x}{x - 1} + \frac{x - 1}{x} = \frac{21}{2}$

$\frac{ {x}^{2} + {(x - 1)}^{2} }{x(x - 1)} = \frac{21}{2}$

$\frac{ {x}^{2} + {x}^{2} - 2.x.1 + {1}^{2} } { {x}^{2} - x } = \frac{21}{2}$

$\frac{2 {x}^{2} - 2x + 1 }{ {x}^{2} - x } = \frac{21}{2}$

$2(2 {x}^{2} - 2x + 1) = 21( {x}^{2} - x)$

$4 {x}^{2} - 4x + 2= 21 {x}^{2} - 21x$

$4 {x}^{2} - 21 {x}^{2} - 4x + 21x + 2= 0$

$- 17 {x}^{2} + 17x + 2 = 0$

$17 {x}^{2} - 17x - 2 = 0 \: \: (multiplying \: both \: sides \: by \: - )$

Answer 2

$\bold\red{We \: have \: x^2+ \frac{1}{2} ^2=23}$

$\bold\red{( \frac{x - 1}{x} )^2=x^2+ \frac{1}{x} ^2−2}$

$[= 23 - 2]</p><p>= 21</p><p>Taking square root on both sides, we get</p><p>[tex]\red( \frac{x - 1}{x} )= \sqrt{21}$

$\bold\red{Thus, \frac{x - 1}{x} = \sqrt{21} \: or \: \sqrt{ -21} }$