To find the answer to "What two numbers have a product of 18 and a sum of 136?" we first state what we know. We are looking for x and y and we know that x • y = 18 and x + y = 136.
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 = 136 and solve it for y to get y = 136 - x. Then, we replace y in x • y = 18 with 136 - x to get this:
x • (136 - x) = 18
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 18 and a sum of 136. The numbers are:
0.13248
135.86752
That's it! The two numbers that have a product of 18 and a sum of 136 are 0.13248 and 135.86752 as proven below:
0.13248 • 135.86752 ≈ 18
0.13248 + 135.86752 = 136
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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