Find all real numbers x such that x2+⌊x2⌋+⌊x3⌋=10.
Not sure how to solve this algebraically, but WolframAlpha gives a solution of -√14
Check
( -√14 )^2 + floor (-√14 / 2) + floor (-√14 / 3 ) =
14 + floor (≈ -1.87) + floor ( ≈ -1.247) =
14 - 2 - 2 =
10
