Not that Easy
Let be the number of real solution(s) to the above equation and be the sum of all real solution(s). Find .
If you think it has no real solution enter 2018.
The answer is -2018.
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1 solution
( 1 + x 1 ) x + 1 ( x x + 1 ) x + 1 ⟹ x = ( 1 + 2 0 1 8 1 ) 2 0 1 8 = ( 2 0 1 8 2 0 1 9 ) 2 0 1 8 = ( 2 0 1 9 2 0 1 8 ) − 2 0 1 8 = ( − 2 0 1 9 − 2 0 1 9 + 1 ) − 2 0 1 9 + 1 = − 2 0 1 9
Therefore, α + β = 1 + ( − 2 0 1 9 ) = − 2 0 1 8 .