Question 1208839
<pre>
{{{sqrt(10 + 3sqrt(x)) = sqrt(x)}}}

Square both sides

{{{10 + 3sqrt(x) = x}}}

Isolate the square root term

{{{3sqrt(x) = x-10}}}

Square both sides

{{{9x = x^2-20x+100}}}

{{{0 = x^2-29x+100}}}

Factor the right side:

{{{0=(x-25)(x-4)}}}

x-25=0;   x-4=0
   x=25;    x=4

Check each potential solution in the original equation:

{{{sqrt(10 + 3sqrt(25)) = sqrt(25)}}}

{{{sqrt(10 + 3*5) = 5}}}

{{{sqrt(10+15)=5}}}

{{{sqrt(25)=5}}}

{{{5=5}}}

So one solution is x = 25     <--ANSWER

Checking x=4

{{{sqrt(10 + 3sqrt(4)) = sqrt(4)}}}

{{{sqrt(10 + 3*2) = 2}}}

{{{sqrt(10+6)=2}}}

{{{sqrt(16)=2}}}

{{{4=2}}}   <--FALSE!

So 4 is NOT a solution.

The only solution is x = 25

Edwin</pre>