For specific positive numbers $m$ and $n$, the quadratics $16x^2+36x+56$ and $(mx+n)^2$ differ only in their constant term. What is $mn$?

Lightning
Jun 10, 2018

#1**+1 **

**For specific positive numbers $m$ and $n$, the quadratics $16x^2+36x+56$ and $(mx+n)^2$ differ only in their constant term. What is $mn$?**

\(\begin{array}{|lrcll|} \hline 16x^2+{\color{red}36}x+56 \\ &&& (mx+n)^2 \\ &&=& m^2x^2+{\color{red}2mn}x+n^2 \\ \Rightarrow & 36 &=& 2mn \\ & mn &=& \frac{36}{2} \\ & \mathbf{mn} & \mathbf{=} & \mathbf{18} \\ \hline \end{array}\)

heureka
Jun 11, 2018