Question 861357: I need explanation and solution:
The product of four consecutive natural numbers is 255024. Find these numbers.
Found 2 solutions by mananth, richwmiller:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! let the natural numbers be x,x+1,x+2,x+3
The product is 255024
x(x+1)(x+2)(x+3)=255024
rearrange
x(x+3)(x+1)(x+2)=255024
(x^2+3x)(x^2+3x+2)=255024
let x^2+3x=a
a(a+2)=255204
a^2+2a= 255024
a^2+2a+1=255024+1
(a+1)^2= 255025
take the square root
(a+1) = +/- 505
a=504 OR -506
substitute a
x^2+3x-504 =0
x^2+24x-21x-504=0
x(x+24)-21(x+24)=0
(x+24)(x-21)=0
x= 21 a natural number
OR
x^2+3x=-506
x^2+3x+506=0
the roots are not real
Hence x=21
21,22,23,24 are the numbers
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! 4th root of 255024 is about 22.47
so 22 or 23 or both are factors
255024/23=11088
11088/22=504
so both 22 and 23 are factors
since we want 4 consecutive numbers the factors must be
20,21,22,23,
21,22,23,24
22,23,24,25
21 or 24 or both are factors
let's test 21
504/21=24
the factors are 21,22,23,24
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