To find the answer to "What two numbers have a product of 1 and a sum of -200?" we first state what we know. We are looking for x and y and we know that x • y = 1 and x + y = -200.
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 = -200 and solve it for y to get y = -200 - x. Then, we replace y in x • y = 1 with -200 - x to get this:
x • (-200 - x) = 1
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 1 and a sum of -200. The numbers are:
-199.995
-0.005
That's it! The two numbers that have a product of 1 and a sum of -200 are -199.995 and -0.005 as proven below:
-199.995 • -0.005 ≈ 1
-199.995 + -0.005 = -200
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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