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1 solution
Let x = 2 0 0 0 . We have 2 0 0 0 × 2 0 0 8 × 2 0 0 9 × 2 0 1 7 + 1 2 9 6 = x ( x + 1 7 ) ( x + 8 ) ( x + 9 ) + 1 2 9 6 = ( x 2 + 1 7 x ) ( x 2 + 1 7 x + 7 2 ) + 1 2 9 6
Let y = x 2 + 1 7 x + 3 6 . ( x 2 + 1 7 x ) ( x 2 + 1 7 x + 7 2 ) + 1 2 9 6 = ( y − 3 6 ) ( y + 3 6 ) + 1 2 9 6 = y 2 = y .
The answer is y = x 2 + 1 7 x + 3 6 = 2 0 0 0 2 + 1 7 × 2 0 0 0 + 3 6 = 4 0 3 4 0 3 6 .