The two numbers are 20 and 36.
Step-by-step explanation:
Finding the Numbers Using the Quadratic Equation
A quadratic equation refers to an equation of the second degree. This means that it contains at least one squared term. The standard form of the quadratic equation is ax² + bx + c = 0 where a, b, and c are being constants, or numerical coefficients, and x is an unknown variable.
Going back to the given problem above, you have to find the two numbers whose difference is 16 and the product is 720. To find the numbers, you have to express the equation in a quadratic equation, then factor it.
Since the two numbers have a difference of 16, you can say that the first number is x and the second number is x + 16. Then, their product is 720.
Solution:
x (x + 16) = 720
x² + 16x = 720 (Equate to 0.)
x² + 16x - 720 = 0 (Factor)
(x + 36) (x - 20)
x = -36 ; x = 20
There are two possible values of x, but since you are looking for the positive value, choose the positive value of x which is 20.
The first number is 20.
Let us now find the second number.
x + 16 = 20 + 16 = 36
The second number is 36.
Final Answer:
The two numbers are 20 and 36.
Checking:
The difference should be 16.
36 - 20 = 16 ✔
The product is 720.
36 × 20 = 720 ✔
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