[Help]Findin all real solution.

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The discussion revolves around solving the equation {1+[x+(2x+1)^1/2]^1/2}^1/2 = (5+x^1/2)^1/2 for the value of x. The poster has attempted squaring both sides but is struggling to find real solutions. Another participant suggests rearranging the equation to analyze the function f(x) and notes that as x approaches infinity, f(x) approaches sqrt(2)/2, indicating that it never reaches 4. This raises doubts about the instructor's claim that there is a large solution for x, suggesting a possible misunderstanding or typo in the problem statement. The conversation highlights the complexity of the equation and the importance of verifying the problem details.
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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:smile:.
 
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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?
 

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