SOLUTION: solve the equation ((x!)!)^2 + ((x!)!) =5040

Question 1199512: solve the equation
((x!)!)^2 + ((x!)!) =5040
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Factorial is only defined for integers, so look for a solution by trying small integer values for x.

By just looking at the first term in the expression, we can quickly see that the equation has no solution.

x = 1: ((1!)!)^2 + ((1!)!) = (1!)^2 + (1!) = 1^2 + 1 = 1 + 1 = 2

x = 2: ((2!)!)^2 + ((2!)!) = (2!)^2 + (2!) = 2^2 + 2 = 4 + 2 = 6

x = 3: ((3!)!)^2 + ((3!)!) = (6!)^2 + (6!) = 720^2 + 720 = 518400 + 720 = 519120

ANSWER: no solution

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