To find the answer to "What two numbers have a product of 82 and a sum of 137?" we first state what we know. We are looking for x and y and we know that x • y = 82 and x + y = 137.
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 = 137 and solve it for y to get y = 137 - x. Then, we replace y in x • y = 82 with 137 - x to get this:
x • (137 - x) = 82
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 82 and a sum of 137. The numbers are:
0.60118
136.39882
That's it! The two numbers that have a product of 82 and a sum of 137 are 0.60118 and 136.39882 as proven below:
0.60118 • 136.39882 ≈ 82
0.60118 + 136.39882 = 137
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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