Question 1177626
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When you guess the solution, then, even if you guessed it correctly,  the question remains if the guessed solution is unique.



Without answering this remaining question,  the solution can not be considered as perfectly correct/completed.


But in this problem, and in many other similar problems, there is a brilliant and cheep way to prove the uniqueness.


Notice that the function    f(x) = x*(2x)*(x+2)    is monotonic in positive domain,

since it is the product of three monotonic functions.



Therefore,  if you guessed   x= 3   as the solution for    x*(2x)*(x+2) = 90,    you can be sure that this solution is unique


(at least,  in the positive domain   x > 0  of real numbers).



So, the guessed solution  x = 3  is a  UNIQUE  solution in the positive domain.



To learn this  TRUTH  is just a good compensation for reading this post.