To find the answer to "What two numbers have a product of 84 and a sum of 22?" we first state what we know. We are looking for x and y and we know that x • y = 84 and x + y = 22.
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 = 22 and solve it for y to get y = 22 - x. Then, we replace y in x • y = 84 with 22 - x to get this:
x • (22 - x) = 84
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 84 and a sum of 22. The numbers are:
4.91724
17.08276
That's it! The two numbers that have a product of 84 and a sum of 22 are 4.91724 and 17.08276 as proven below:
4.91724 • 17.08276 ≈ 84
4.91724 + 17.08276 = 22
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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