Answer:
5 and 8
Explanation:
One number is 3 greater than another. The product of the numbers is 40. Find the numbers
Let's call the smaller number "x". Then we know that the larger number is 3 more than x, so we can call it "x+3". We also know that the product of the two numbers is 40, so:
x(x+3) = 40
Expanding the left side of the equation, we get:
x^2 + 3x = 40
Subtracting 40 from both sides, we get:
x^2 + 3x - 40 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 3, and c = -40. Plugging these values in, we get:
x = (-3 ± sqrt(3^2 - 4(1)(-40))) / 2(1)
x = (-3 ± sqrt(169)) / 2
So x is either:
x = (-3 + 13) / 2 = 5
or
x = (-3 - 13) / 2 = -8
We can check these values by verifying that x+3 is indeed 3 more than x, and that their product is indeed 40. We see that only the first solution, x=5, satisfies these conditions:
The two numbers are 5 and 8.