Question

the product of three consecutive integers is 30 times the smallest of the three integers. find the two possible sets of integers that will satisfy this condition.

Answer 1

$\textbf{Given:}$

$\textsf{Product of 3 consecutive integers is 30 times smallest}$

$\textsf{of the three integers}$

$\textbf{To find:}$

$\textsf{The three integers}$

$\textbf{Solution:}$

$\textsf{Let the three consecutive integers be x, x+1 and x+2}$

$\mathsf{As\;per\;given\;data,}$

$\mathsf{x(x+1)(x+2)=30x}$

$\implies\mathsf{(x+1)(x+2)=30}$

$\implies\mathsf{x^2+3x+2=30}$

$\implies\mathsf{x^2+3x-28=0}$

$\implies\mathsf{(x+7)(x-4)=0}$

$\implies\mathsf{x=-7,4}$

$\mathsf{when\,x=4,}$

$\underline{\mathsf{The\;integers\;are\;4,\;5,\;6}}$

$\mathsf{when\,x=-7,}$

$\underline{\mathsf{The\;integers\;are\;-7,\;-6,\;-5}}$

$\textbf{Find more:}$

Product of any four consecutive positive integers is divisible by 24

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