Question

x!(x+1)!=20
--------------
(x-1)!(x)!

Answer 1

x!(x+1)!

-------------- = 20

(x-1)!(x)!

(x+1)!

----------------------- = 20

(x-1)!

(x+1).x.(x-1)!

--------------------- = 20

(x-1)!

(x+1) x = 20

x² + x - 20 = 0

∆=1² -4.1.(-20)= 1 +80= 81 => √∆=9

x' = -b+√∆/2a = -1+9/2 = 8/2 = 4 ✓