(i) The product of four consecutive natural
numbers is 840. Find the numbers.
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Step-by-step explanation:
Let the consecutive numbers be n, (n+1) , (n + 2 ) (n+ 3).
Given that their product = 840
then n(n+1)(n + 2 )(n+ 3) = 840.
this can also written as n(n+3)⋅(n+1)(n+2) = 840
Add and subtarct 1 to the first number of the product.
((n^2+3n+1)−1)((n2+3n+1)+1) = 840
(n^2+3n+1)^2−1 = 840
(n^2+3n+1)^2 = 841
(n^2+3n+1)^2 = 29 ^2
(n^2+3n+1) = 29 implies n^2+3n+1–29=0 = n^2 + 3n - 28
(n + 7) (n - 4) = 0
if n = 4 we have 4, 5, 6, 7 n = -7 is not possible -7 does not belongs to the natural number
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