Question 633735
√(x)+(√(x-3)=3
<pre>
{{{sqrt(x)}}} + {{{sqrt(x-3)}}} = 3

Isolate one of the terms with a radical 
(preferably the more complicated one)

       {{{sqrt(x-3)}}} = 3 - {{{sqrt(x)}}}

Square both sides:

    ({{{sqrt(x-3)}}})² = (3 - {{{sqrt(x)}}})²

        x - 3 = (3 - {{{sqrt(x)}}})(3 - {{{sqrt(x)}}})

        x - 3 = 9 - 3{{{sqrt(x)}}} - 3{{{sqrt(x)}}} + x

        x - 3 = 9 - 6{{{sqrt(x)}}} + x

Simplify and isolate the term with the radical

        6{{{sqrt(x)}}} = 12

Divide both sides by 6

         {{{sqrt(x)}}} = 2

Square both sides

        ({{{sqrt(x)}}})² = 2²

         x = 4

We must always check for extraneous (false) solutions
because squaring both sides often introduces them.

{{{sqrt(x)}}} + {{{sqrt(x-3)}}} = 3
{{{sqrt(4)}}} + {{{sqrt(4-3)}}} = 3
       2 + {{{sqrt(1)}}} = 3
         2 + 1 = 3
             3 = 3

So x = 4 is the solution.

Edwin</pre>