Answer to Question #33120 in Algebra for Mano

Question

the sum of two numbers is 18 and thier product is 65. find the numbers.

Answer 1

Let the first number is a, the second is b. So we have:
a+b=18, ab=65
From the first equation a=18-b. Substituting it instead of a into the second equation we obtain:
(18-b)b=65
18b-b^2=65
b^2-18b+65=0
Solving it for b we get:
b=5 or b=13.
So for a we have the next options: a=13 or a=5
Answer: the umbers are 13 and 5.