Find two positive numbers whose difference is 8

and whose product is 425
.

1 answer

Let the two positive numbers be x and y.

According to the given conditions, we can set up two equations:
1. x - y = 8
2. xy = 425

From equation 1, we can rewrite it as x = 8 + y and substitute it into equation 2:

(8 + y)y = 425

Expanding and rearranging the equation, we get:
8y + y^2 = 425
y^2 + 8y - 425 = 0

Now we can solve this quadratic equation for y by factorization, completing the square, or using the quadratic formula. In this case, we see that the equation factors as:

(y – 17)(y + 25) = 0

Setting each factor equal to zero:
y - 17 = 0 or y + 25 = 0

Solving these equations, we find two possible values for y:
y = 17 or y = -25

Since we need to find positive numbers, we discard the negative value. Therefore, y = 17.

Now we can substitute this value back into equation 1 to solve for x:
x - 17 = 8
x = 8 + 17
x = 25

So the two positive numbers are 25 and 17, as their difference is 8 and their product is 425.