To find the answer to "What two numbers have a product of 13 and a sum of 114?" we first state what we know. We are looking for x and y and we know that x • y = 13 and x + y = 114.
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 = 114 and solve it for y to get y = 114 - x. Then, we replace y in x • y = 13 with 114 - x to get this:
x • (114 - x) = 13
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 13 and a sum of 114. The numbers are:
0.11415
113.88585
That's it! The two numbers that have a product of 13 and a sum of 114 are 0.11415 and 113.88585 as proven below:
0.11415 • 113.88585 ≈ 13
0.11415 + 113.88585 = 114
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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