Question

the product of four concesutive natural number is 3024 find the numbers

Answer 1

Let the numbers be x, x + 1, x + 2, x + 3 
=> x(x + 1)(x + 2)(x + 3) = 3024 
=> x(x + 3)(x + 2)(x + 1) = 3024 
=> (x² + 3x)(x² + 3x + 2) = 3024 
Let x² + 3x = k 
=> k(k + 2) = 3024 
=> k² + 2k = 3024 
=> k² + 2k - 3024 = 0 
=> k = [-2 ± √(12100)] / 2 
=> k = -1 ± 55 
=> k = -56, 54 
=> x² + 3x = -56, 54 

.·. 
x² + 3x = -56 
=> x² + 3x + 56 = 0 
=> b² - 4ac < 0 

x² + 3x = 54 
=> x² + 3x - 54 = 0 
=> x² + 9x - 6x - 54 = 0 
=> (x + 9)(x - 6) = 0 
=> x = -9, 6 
=> x = 6 since x is +ve 
=> numbers are 6, 7, 8, 9