The sum of two numbers is 19 and the prouduct is 78 what is the smaller number
let one number be x
then the other be 19-x
x(19-x) = 78
19x - x^2 = 78
x^2 - 19x + 78 = 0
(x-6)(x-13) = 0
x = 6 or x = 13
so the smaller is 6, the larger is 19-6 or 13
s = smaller number
l = larger number
s + l = 19
Subtract s to both sides.
l = 19 - s
s • l = 78
s ( 19 - s ) = 78
19 s - s² = 78
Subtract 78 to both sides.
- s² + 19 s - 78 = 0
Multiply both sides by - 1
s² - 19 s + 78 = 0
The solutions are:
s = 6 and s = 13
For s = 6
l = 19 - s = 19 - 6 = 13
For s = 13
l = 19 - s = l = 19 - 13 = 6
A larger number cannot be less than a smaller number.
That's why the larger number = 13
The smaller number = 6