Question 712174
<pre>
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(7-2x)-sqrt(x+2)}}}{{{""=""}}}{{{sqrt(x+5)}}}

Checking {{{10/3}}}

{{{sqrt(7-2(10/3))-sqrt((10/3)+2)}}}{{{""=""}}}{{{sqrt((10/3)+5)}}}

{{{sqrt(21/3-20/3)-sqrt(10/3+6/3)}}}{{{""=""}}}{{{sqrt(10/3+15/3)}}}

{{{sqrt(1/3)-sqrt(16/3)}}}{{{""=""}}}{{{sqrt(25/3)}}}

{{{sqrt(1/3)-4sqrt(1/3)}}}{{{""=""}}}{{{5sqrt(1/3)}}}

That does not check.  So {{{10/3}}} is NOT a solution,
it is EXTRANEOUS.

Checking -1

{{{sqrt(7-2(-1))-sqrt((-1)+2)}}}{{{""=""}}}{{{sqrt((-1)+5)}}}

{{{sqrt(7+2)-sqrt(1)}}}{{{""=""}}}{{{sqrt(4)}}}


{{{sqrt(9)-1}}}{{{""=""}}}{{{2}}}

{{{3-1}}}{{{""=""}}}{{{2}}}

{{{2}}}{{{""=""}}}{{{2}}}

So there is just one solution, -1.

Edwin</pre>