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What two numbers would have a product of 108 and a sum of 23 at the same time?
Wiki User
∙ 12y ago
Here's one way to work that out. Let's call the numbers "a" and "b" We're told:
a + b = 23
ab = 108
We can take one of those two, solve it for either a or b, substitute it into the other, and solve for the other variable using our new equation:
a + b = 23
b = 23 - a
∴ a(23 - a) = 108
-a2 + 23a = 108
a2 - 23a + 108 = 0
a2 - 23a + (23/2)2 = (23/2)2 - 108
(a - 23/2)2 = 529/4 - 432/4
(a - 23/2)2 = 97/4
a - 23/2 = ± √(97/4)
a = (23 ± √97) / 2
So the two numbers that meet this condition are (23 - √97) / 2 and (23 + √97) / 2
Wiki User
∙ 12y ago
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