To find the answer to "What two numbers have a product of 105 and a sum of 102?" we first state what we know. We are looking for x and y and we know that x • y = 105 and x + y = 102.
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 = 102 and solve it for y to get y = 102 - x. Then, we replace y in x • y = 105 with 102 - x to get this:
x • (102 - x) = 105
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 105 and a sum of 102. The numbers are:
1.04002
100.95998
That's it! The two numbers that have a product of 105 and a sum of 102 are 1.04002 and 100.95998 as proven below:
1.04002 • 100.95998 ≈ 105
1.04002 + 100.95998 = 102
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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