Answer:
The two positive integers are 30 and 30
Step-by-step explanation:
Let
x------> the larger positive integer
y-----> the smaller positive integer
P----> the product o the two positive integers
we know that
![x+y=60](https://tex.z-dn.net/?f=x%2By%3D60)
-----> equation A
----> equation B
substitute equation A in equation B
![P=60x-x^{2}](https://tex.z-dn.net/?f=P%3D60x-x%5E%7B2%7D)
This is the equation of a vertical parabola open downward
The vertex is a maximum
The y-coordinate of the vertex is the largest possible product
Using a graphing tool
The vertex is the point (30,900)
That means------> For
The largest possible product is ![900](https://tex.z-dn.net/?f=900)
and
------> ![y=60-30=30](https://tex.z-dn.net/?f=y%3D60-30%3D30)
therefore
The two positive integers are 30 and 30