SOLUTION: Find the real solutions of the radical equation. sqrt{(10+ 3•sqrt{x})} = sqrt{x} Note: (10 + 3•sqrt{x}) lies inside a bigger radicand.

Algebra ->  Radicals -> SOLUTION: Find the real solutions of the radical equation. sqrt{(10+ 3•sqrt{x})} = sqrt{x} Note: (10 + 3•sqrt{x}) lies inside a bigger radicand.       Log On


   

Question 1208839: Find the real solutions of the radical equation.

sqrt{(10+ 3•sqrt{x})} = sqrt{x}

Note: (10 + 3•sqrt{x}) lies inside a bigger radicand.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2810+%2B+3sqrt%28x%29%29+=+sqrt%28x%29

Square both sides

10+%2B+3sqrt%28x%29+=+x

Isolate the square root term

3sqrt%28x%29+=+x-10

Square both sides

9x+=+x%5E2-20x%2B100

0+=+x%5E2-29x%2B100

Factor the right side:

0=%28x-25%29%28x-4%29

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

Check each potential solution in the original equation:

sqrt%2810+%2B+3sqrt%2825%29%29+=+sqrt%2825%29

sqrt%2810+%2B+3%2A5%29+=+5

sqrt%2810%2B15%29=5

sqrt%2825%29=5

5=5

So one solution is x = 25     <--ANSWER

Checking x=4

sqrt%2810+%2B+3sqrt%284%29%29+=+sqrt%284%29

sqrt%2810+%2B+3%2A2%29+=+2

sqrt%2810%2B6%29=2

sqrt%2816%29=2

4=2   <--FALSE!

So 4 is NOT a solution.

The only solution is x = 25

Edwin