Question

The sum of two numbers is 15. twice the product of the two numbers is 108. What are the 2 numbers?

Answer 1

`\begin{gathered} x+y=15\rightarrow x=15-y\text{ } \\ 2x\cdot y=108\rightarrow x\cdot y=54 \\ \text{if we replace x=15-y in the second equation we get} \\ (15-y)\cdot y=54 \\ 15y-y^2=54\rightarrow y^2-15y+54=0 \\ y^2-15y+54=(y-6)(y-9)=0 \\ y=6\text{ }\lor y=9 \\ \text{if y}=6\rightarrow x=15-6=9\text{ and} \\ \text{if y=9}\rightarrow x=15-9=6 \end{gathered}`