Find two integers whose sum is 16 and product is 64
Answers
Answer:
8
8+8=16
and
8*8=64
So the integers are 8,8
Step-by-step explanation:
To find the answer to "What two numbers have a product of 64 and a sum of 16?" we first state what we know. We are looking for x and y and we know that x • y = 64 and x + y = 16.
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 = 16 and solve it for y to get y = 16 - x. Then, we replace y in x • y = 64 with 16 - x to get this:
x • (16 - x) = 64
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 64 and a sum of 16. The numbers are:
8
8
That's it! The two numbers that have a product of 64 and a sum of 16 are 8 and 8 as proven below:
8 • 8 = 64
8 + 8 = 16
Note: Answers are rounded up to the nearest 6 decimals if necessary so the answers may not be exact.