Question

The sum of 2 numbers is 14. The product is 40. What is the largest of numbers?

Answer 1

a + b = 14

a * b = 40


a + b = 14 Subtract a to both sides

a + b - a = 14 - a

b = 14 - a


a * b = 40

a * ( 14 - a ) = 40

14 a - a ^ 2 = 40

- a ^ 2 + 14 a = 40 Subtract 40 to both sides

- a ^ 2 + 14 a - 40 = 40 - 40

- a ^ 2 + 14 a - 40 = 0 Multiply both sides by - 1

a ^ 2 - 14 a + 40 = 0

The solutions are:

a = 4 and a = 10

For a = 10

b = 14 - a = 14 - 10 = 4


For a = 4

b = 14 - 4 = 10

The numbers are:

4 and 10


4 + 10 = 14

4 * 10 = 40

Answer 2

one number ---- x , the larger
the other --- 14-x

x(14-x) = 40
14x - x^2 = 40
x^2 - 14x + 40 = 0

(x-10)(x-4) = 0
x = 10 or x = 4

the two numbers are 10 and 4.