Question 1091925
.
<pre>
{{{x}}} + {{{1/x}}} = 8  ====> multiply both sides by x  ====>

{{{x^2 + 1}}} = 8x  ====>  collect x-terms on the left side. Move the constant term to the right side  ====>

{{{x^2 - 8x}}} = -1  ====>  add 16 to both sides  ====>

{{{x^2 - 2*4x + 16}}} = -1 + 16  ====>  complete the square on the left side  ====>

{{{(x-4)^2}}} = 15  ====>  take the saure root from both sides  ====>

x - 4 = +/- {{{sqrt(15)}}}.


<U>Answer</U>.  There are two solutions:   {{{4 + sqrt(15)}}}  and  {{{4-sqrt(15)}}}.
</pre>

Solved.


I applied the completing the square method to solve the quadratic equation.


To learn more about this method, see the leson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-solve-quadratic-equation-by-completing-the-square-Learning-by-examples.lesson>HOW TO solve quadratic equation by completing the square - Learning by examples</A> 

in this site.