To find the answer to "What two numbers have a product of 34 and a sum of 196?" we first state what we know. We are looking for x and y and we know that x • y = 34 and x + y = 196.
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 = 196 and solve it for y to get y = 196 - x. Then, we replace y in x • y = 34 with 196 - x to get this:
x • (196 - x) = 34
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 34 and a sum of 196. The numbers are:
0.17362
195.82638
That's it! The two numbers that have a product of 34 and a sum of 196 are 0.17362 and 195.82638 as proven below:
0.17362 • 195.82638 ≈ 34
0.17362 + 195.82638 = 196
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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