Question

all solutions to

\[x^2=\left[ x^3 \right]\]

Answer 1

[] is floor function

Answer 2

x=0 (trivial case) and x=1

Answer 3

missed one of the answers...

Answer 4

2 = 2 gives sqrt 2

Answer 5

lol....u got it...

Answer 6

3 = 3 => sqrt 3
http://www.wolframalpha.com/input/?i=floor [3sqrt+3]
seems sqrt 3 is not the solution ... since the left side is of order ^3 .. and right side is of ^2 ... there cannot be any other solution.
on the other hand .. left side is even function and right side is odd .. so there aren't any integers on negative side.

Answer 7

simply \(x>2\) and \(x<0\) are not answers...

and \(x^2\) must be an integer so we have 4 cases to check \(x=0,1,\sqrt{2},\sqrt{3}\)