To find the answer to "What two numbers have a product of 61 and a sum of -68?" we first state what we know. We are looking for x and y and we know that x • y = 61 and x + y = -68.
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 = -68 and solve it for y to get y = -68 - x. Then, we replace y in x • y = 61 with -68 - x to get this:
x • (-68 - x) = 61
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 61 and a sum of -68. The numbers are:
-67.09078
-0.90922
That's it! The two numbers that have a product of 61 and a sum of -68 are -67.09078 and -0.90922 as proven below:
-67.09078 • -0.90922 ≈ 61
-67.09078 + -0.90922 = -68
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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