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One positive integer is two less than twice the other. The product of the two is 84. Find the integers

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LammettHash

\(x=2y-2\)
\(xy=84\)

Plug the first equation into the second to get

\((2y-2)y=2y^2-2y=84\implies 2y^2-2y-84=0\implies y^2-y-42=(y-7)(y+6)=0\)

It's clear that both integers are positive, so it must be the case that \(y=7\), which means \(x=12\).

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