To find the answer to "What two numbers have a product of 19 and a sum of 84?" we first state what we know. We are looking for x and y and we know that x • y = 19 and x + y = 84.
Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which means that when we create one equation to solve the problem, we will have two answers.
To solve the problem, we take x + y = 84 and solve it for y to get y = 84 - x. Then, we replace y in x • y = 19 with 84 - x to get this:
x • (84 - x) = 19
Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 19 and a sum of 84. The numbers are:
0.2268
83.7732
That's it! The two numbers that have a product of 19 and a sum of 84 are 0.2268 and 83.7732 as proven below:
0.2268 • 83.7732 ≈ 19
0.2268 + 83.7732 = 84
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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