[Help]Findin all real solution.

[studenlearner]

Hello guys, I need help with my homework.
The problem is I need to find the value/s of x given this equation:

{1+[x+(2x+1)^1/2]^1/2}^1/2 = (5+x^1/2)^1/2

I've tried to square both sides but still no avail. But our instructor told us the value of "x" is a large number.Any help is much welcomed.

 

[Dick]

I don't think there are any real solutions. Square it once and rearrange it into sqrt(x+sqrt(2x+1))-sqrt(x)=4. Now call f(x) the left side of that equation. Can you show the limit as x->infinity of f(x) is sqrt(2)/2? If you put that together with a graph of f(x) for small numbers it's pretty clear f(x) never reaches 4. Are you sure your instructor didn't say look at the behavior for large 'x', rather than that the solution was a large value of 'x'? Or is there a typo in the equation?