Explanation
In the question, we are asked to find two positive numbers whose Difference is two and whose product is 1443.
If we let the numbers be x and y, therefore we can create the equation below,
[tex]\begin{gathered} x-y=2\text{ ------(1)} \\ xy=1443-----(2) \end{gathered}[/tex]
But;
[tex]x=y+2----(3)[/tex]
Substitute equation 3 in equation 2
[tex]\begin{gathered} y(y+2)=1443 \\ y^2+2y=1443 \\ y^2+2y-1443=0 \end{gathered}[/tex]
Using the quadratic formula;
[tex]\begin{gathered} y=_{}\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where a =1, b=2 and c=-1443} \end{gathered}[/tex]
Therefore;
[tex]\begin{gathered} y_{1,\: 2}=\frac{-2\pm\sqrt[]{2^2-4\times\: 1\times\mleft(-1443\mright)}}{2\times\: 1} \\ y_{1,\: 2}=\frac{-2\pm\: 76}{2\times\: 1} \\ y_1=\frac{-2+76}{2\times1}=37 \\ y_2=\frac{-2-76}{2\times\: 1}=-39 \end{gathered}[/tex]
Since we need only the positive value, we will substitute y=37 in equation three.
[tex]\begin{gathered} x=37+2 \\ x=39 \end{gathered}[/tex]
Answer: The two numbers are 37 and 39
