Question

The sum of two numbers is 17 and their product is 66 what are the two numbers.

Answer 1

11 and 6

Explanation:

x + y = 17

x × y = 66

First, solve for y

x + y = 17

x + y - x = 17 - x

y = 17 - x

Then substitute y to x × y = 66

x × y = 66

x(17 - x) = 66

17x -
`x^(2)` - 66 = 66 - 66

-
`x^(2)` + 17x - 66 = 0

(-
`x^(2)` + 17x - 66) = 0

(-x + 6)(x - 11) = 0

-x + 6 = 0

-x + x +6 = 0 + x

6 = x or x = 6

x - 11 = 0

x - 11 +11 = 0 + 11

x = 11

Then the numbers are 11 and 6

Answer 2

11 and 6

Explanation:

Let the numbers be X and Y

Then their sum: X+Y=17 equation 1

Product: X×Y=66 equation 2

X+Y=17. X =17-Y

XY=66.

(17-Y)Y=66 -Y²+17Y-66=0

Y=6 or 11

X=17-Y. X=17–6=11 or X=17–11=6

Therefore you can conclude that the numbers are 11&6