To find the answer to "What two numbers have a product of 180 and a sum of 62?" we first state what we know. We are looking for x and y and we know that x • y = 180 and x + y = 62.
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 = 62 and solve it for y to get y = 62 - x. Then, we replace y in x • y = 180 with 62 - x to get this:
x • (62 - x) = 180
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 180 and a sum of 62. The numbers are:
3.05362
58.94638
That's it! The two numbers that have a product of 180 and a sum of 62 are 3.05362 and 58.94638 as proven below:
3.05362 • 58.94638 ≈ 180
3.05362 + 58.94638 = 62
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
Product Sum Calculator
Need the answer to a similar problem? Submit another product and sum below to find the two numbers that make your product and sum.