To find the answer to "What two numbers have a product of 3 and a sum of -5?" we first state what we know. We are looking for x and y and we know that x • y = 3 and x + y = -5.
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 = -5 and solve it for y to get y = -5 - x. Then, we replace y in x • y = 3 with -5 - x to get this:
x • (-5 - x) = 3
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 3 and a sum of -5. The numbers are:
-4.30278
-0.69722
That's it! The two numbers that have a product of 3 and a sum of -5 are -4.30278 and -0.69722 as proven below:
-4.30278 • -0.69722 ≈ 3
-4.30278 + -0.69722 = -5
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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