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
[tex]x+y=60[/tex]
[tex]y=60-x[/tex] -----> equation A
[tex]P=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]P=x(60-x)[/tex]
[tex]P=60x-x^{2}[/tex]
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 [tex]x=30[/tex] The largest possible product is [tex]900[/tex]
and
[tex]y=60-x[/tex] ------> [tex]y=60-30=30[/tex]
therefore
The two positive integers are 30 and 30
