Question 1132586
<pre>
Sorry that's not true.

Here is a case where it's false:

suppose a=2, b=1, then

{{{x=sqrt(sqrt(a/b)-sqrt(b/a))}}} 

{{{x=sqrt(sqrt(2/1)-sqrt(1/2))}}}

Putting the right side in your calculator you get

x=0.8408964153

Then a=2, b=1 and x=0.8408964153

{{{(2a)sqrt(1+x^2)/(x+sqrt(1+x^2))=a+b}}}

{{{(2*2)sqrt(1+0.8408964153^2)/(0.8408964153+sqrt(1+0.8408964153^2))=2+1}}}

Putting that in your calculator gives

{{{2.433690671=3}}}

which is clearly false.

Edwin</pre>