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1 solution
Perhaps this will help someone interested in seeing a solution: this link leads to math.stackexchange.com
Since ( 2 + 3 ) 2 0 1 2 + ( 2 − 3 ) 2 0 1 2 is an integer (which is shown via an application of the binomial theorem at the provided link) and 2 − 3 < 1 , we have f = 1 − ( 2 − 3 ) 2 0 1 2 .
Therefore, x ( 1 − f ) = ( 2 + 3 ) 2 0 1 2 ( 1 − ( 1 − ( 2 − 3 ) 2 0 1 2 ) ) = ( 2 + 3 ) 2 0 1 2 ( 2 − 3 ) 2 0 1 2 = ( 4 − 3 ) 2 0 1 2 = 1