surgrimpig3x

2022-02-05

The product of two integers is 75 and their sum is -28. What are the two integers?

deliria1t4

-3 and -25
Explanation:
Let the integers be m and n with $|m|\le |n|$
Since $mn=75$ is positive, m and n are either both positive or both negative.
If m and n were both positive, then $m+n$ would be positive too, but $m+n=-28$, so m and n are both negative.
$75=3\cdot 5\cdot 5$
so (m, n) must be one of:
$\left(-1,-75\right),\left(-3,-25\right),\left(-5,-15\right)$
Of these only $\left(m,n\right)=\left(-3,-25\right)$ gives us $m+n=-28$.

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