The two numbers are represented by x and 8 - x. By setting x * (8 - x) = 80, we obtain a quadratic equation which can be solved using the Quadratic formula to find x = 2 and x = -40. However, we ignore the negative solution as we're dealing with positive numbers, resulting in 2 and 6 as the two numbers.
First, let's identify the two numbers. Let's let x represent one of these numbers. Because we're told that the sum of the two numbers is 8, we can express the second number as 8 - x.
Next, let's use this information to write our equation. We're told that the product of our two numbers is 80. In terms of x, we can write this as: x * (8 - x) = 80. Simplify this to obtain the quadratic equation: -x^2 + 8x - 80 = 0.
From this, we can apply the Quadratic Formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). Substituting a = -1, b = 8, and c = -80 into the formula, we find the solutions are x = 2 and x = -40. However, since we're dealing with positive numbers here, we can ignore the negative solution, leaving us with the two numbers as 2 and 6.
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