The positive difference between these two numbers is ∣8−9∣=1.
Let x and y be the two positive real numbers.
Given:
x+y=17
xy=40
We want to find the positive difference between these two numbers, which is ∣x−y∣.
Let's solve for x and y using these equations:
From x+y=17, we can express y in terms of x as y=17−x.
Substituting this expression for y into the equation xy=40:
x(17−x)=40
17x−x^2 =40
x^2 −17x+40=0
Now, let's factorize or use the quadratic formula to solve for x:
x^2 −17x+40=0
(x−8)(x−9)=0
Setting each factor equal to zero:
x−8=0 or x−9=0
x=8 or x=9
So, the two numbers are x=8 and y=17−x=17−8=9 or x=9 and y=17−x=17−9=8.
Therefore, the positive difference between these two numbers is ∣8−9∣=1.