Question

If $\frac{x^2+1}{x}=2\frac{1}{2}$ , find the value of:
$x-\frac{1}{x}$

Answer 1

Given,

$\frac{x^2+1}{x}=2\cdot \frac{1}{2}$

$\frac{x^2+1}{x}=\frac{5}{2}$

$2x^2+2=5x$

$2x^2-5x+2=0$

$(x-2)(2x-1)=0$

$x=2,\frac{1}{2}$

(i)

$x-\frac{1}{x}$

$=2-\frac{1}{2}$

$=\frac{3}{2}$

(ii)

$x-\frac{1}{x}$

$=\frac{1}{2}-2$

$=-\frac{3}{2}$