Pls help me solve this equation!

[nakamoto2305]

$x\sqrt{x+1}+(x+5)\sqrt{x+6}=x^2+4x+9$

I find out that there is only 1 solution is x=3. I tried to use derivative but it's too complex, can somebody help me find a way to solve it?

 

[nasi112]

And why do you think that there is a second solution?

 

[Deleted member 4993]

$x\sqrt{x+1}+(x+5)\sqrt{x+6}=x^2+4x+9$

I find out that there is only 1 solution is x=3. I tried to use derivative but it's too complex, can somebody help me find a way to solve it?

Did you try using graphical method?

Are you supposed to prove that there is only ONE solution?

 

[Dr.Peterson]

I find out that there is only 1 solution is x=3.

This sentence is unclear. Do you mean that you found the solution x=3, and wonder if there is another, or that you are required to find the solution, and were told that the only solution is x=3, or something else?

Also, it will help if you tell us the context of the problem. If it is for a course, what topics have been taught that you might be expected to use? If it is for a contest or something like that, what level is it at? Also, why do you think the derivative will help in solving (or in proving uniqueness)?

And can you show the work you did to accomplish whatever you have done so far?

 

[lookagain]

$x\sqrt{x+1}+(x+5)\sqrt{x+6}=x^2+4x+9$

I find out that there is only 1 solution is x=3. I tried to use derivative but it's too complex, can somebody help me find a way to solve it?

nakamoto2305, here is a specific question. In the context of the problem, did it make mention if you are/were to be solving
for only integer values, rational values, or all real values of x, for example?