(x+2)! (2x+1)! /(2x - 1)! (x+3)! =72/7 solve the equation x belong to N
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Answer:
(2x−1)!
(x+2)!
.
(x+3)!
(2x+1)!
=
7
72
(2x+1)! = (2x+1)(2x)(2x-1)!
(x+3)! = (x+3)(x+2)!
using these
(2x+1)(2x) /(x+3) = 72/7
=> (4x² + 2x)7 = 72(x+3)
=> 28x² + 14x = 72x + 216
=> 28x² - 58x - 216 = 0
=> 14x² - 29x - 108 = 0
=> 14x² -56x + 27x - 108 = 0
=>14x(x-4) + 27(x-4) = 0
=> (14x + 27)(x-4) = 0
=> x = 4 , x = -27/14 ( can not be negative)
x = 4
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