Japanese Math Olympiad 

(x+4)!/(x+1)!=720 (x+4)(x+3)(x+2)=720 Let y=x+3 --> (y+1)y(y-1)=720 =10×9×8 y=9 --> x=6

x = 6

( x + 4) ( x + 3) ( x + 2) = 720 = 10* 9 * 8 ( x + 3 ) ( ( x + 3) ^2 - 1) = 10 * 9 * 8 ( x + 3) ^3 - ( x + 3) = 9 ^ 3 - 9 ( x + 3 - 9) ( ( x +3) ^2 + ( x +3) +1) - ( x + 3 - 9) = 0 ( x - 6) ( (x+3) ^2 + ( x +3) + 1 -1) = 0 ( x -6) ( ( x +3) ^2 + ( x +3)) = 0 x = 6, - 3 , - 1 x = 6 is only feasible solution

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