SOLUTION: sqrt(7-2x)-sqrt(x+2)=sqrt(x+5) I have completed this problem by isolating and removing the radicals and so on, but I do not think the answer I got is correct. The answer I got was

Algebra ->  Radicals -> SOLUTION: sqrt(7-2x)-sqrt(x+2)=sqrt(x+5) I have completed this problem by isolating and removing the radicals and so on, but I do not think the answer I got is correct. The answer I got was      Log On


   

Question 712174: sqrt(7-2x)-sqrt(x+2)=sqrt(x+5)
I have completed this problem by isolating and removing the radicals and so on, but I do not think the answer I got is correct. The answer I got was x=10/-3 or x=-1.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(7-2x)-sqrt(x+2)=sqrt(x+5)
--------------
7-2x + x+2 - 2sqrt()sqrt() = x+5
-2x + 4 = 2sqrt()sqrt()
-x+2 = sqrt()sqrt()
x^2 - 4x + 4 = (7-2x)*(x+2)
x%5E2+-+4x+%2B+4+=+-2x%5E2+%2B+3x+%2B+14
3x%5E2+-+7x+-+10+=+0
x = 7/6 ± 13/6
x = -1, 10/3
==========
+10/3

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor solved correctly, but FAILED TO check 
the two answers he got!  But you MUST CHECK!!!

When you square both sides of an equation, you may get
extraneous answers so you MUST check such answers to
see if they really are solutions.

sqrt%287-2x%29-sqrt%28x%2B2%29%22%22=%22%22sqrt%28x%2B5%29

Checking 10%2F3

sqrt%287-2%2810%2F3%29%29-sqrt%28%2810%2F3%29%2B2%29%22%22=%22%22sqrt%28%2810%2F3%29%2B5%29

sqrt%2821%2F3-20%2F3%29-sqrt%2810%2F3%2B6%2F3%29%22%22=%22%22sqrt%2810%2F3%2B15%2F3%29

sqrt%281%2F3%29-sqrt%2816%2F3%29%22%22=%22%22sqrt%2825%2F3%29

sqrt%281%2F3%29-4sqrt%281%2F3%29%22%22=%22%225sqrt%281%2F3%29

That does not check.  So 10%2F3 is NOT a solution,
it is EXTRANEOUS.

Checking -1

sqrt%287-2%28-1%29%29-sqrt%28%28-1%29%2B2%29%22%22=%22%22sqrt%28%28-1%29%2B5%29

sqrt%287%2B2%29-sqrt%281%29%22%22=%22%22sqrt%284%29


sqrt%289%29-1%22%22=%22%222

3-1%22%22=%22%222

2%22%22=%22%222

So there is just one solution, -1.

Edwin