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Find Function From Fraction (Posted on 2016-09-22) Difficulty: 3 of 5
Determine all possible real numbers x satisfying the equation:

F((x+1)3) = x3, where F(x) = x – floor(x)

No Solution Yet Submitted by K Sengupta    
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*** edited to show correct argument of floor function in solution.

F((x+1)3) = x3, where F(x) = x - floor(x)

0 <= F(x) < 1, so 0 <= x < 1

F((x+1)3) = x+ 3x+ 3x + 1 - floor((x+1)3) = x3

floor((x+1)3) =3x+ 3x + 1 = 3(x+ x) + 1, an integer >=0 and < 7 as x < 1

x+ x = 5/3, x = -1/2+sqrt(23/3)/2
x+ x = 4/3, x = -1/2+sqrt(19/3)/2
x+ x = 1, x = -1/2+sqrt(5)/2
x+ x = 2/3, x = -1/2+sqrt(11/3)/2
x+ x = 1/3, x = -1/2+sqrt(7/3)/2
x+ x = 0, x = 0

Edited on September 27, 2016, 6:29 pm

Edited on September 27, 2016, 6:30 pm
  Posted by ken on 2016-09-27 13:43:49

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