An algebra problem by Soha Abdelbassir
Algebra
Level
1
(2X)! = X! . (X+2)!
Find the value of X
NB:
5! = 5×4×3×2×1 = 120
6! = 6×5×4×3×2×1 = 720
The answer is 3.
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1 solution
(2X)! = X! . (X+2)!
2X . (2X-1)! = X . (X-1)! . (X+2)!
(2X-1)! / (X-1)! = (X+2)! / 2
(2X-1)PX = (X+2)PX
Then
2X-1 = X+2
X = 3
NB:
5P3 = 5×4×3
5P2 = 5×4
6P4 = 6×5×4×3