Question

Which two numbers have a sum of 15 and a product of 36

Answer 1

3 and 12

Explanation:

let the 2 numbers be x and y then

x + y = 15 → (1)

xy = 36 → (2)

From (1) : y = 15 - x → (3)

substitute y = 15 - x into (2)

x(15 - x) = 36

15x - x² = 36 ( subtract 36 from both sides )

15x - x² - 36 = 0 ( multiply through by - 1 and arrange in standard form )

x² - 15x + 36 = 0 ← in standard form

(x - 3)(x - 12) = 0 ← in factored form

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 12 = 0 ⇒ x = 12

substitute these values into (3) for corresponding value of y

x = 3 → y = 15 - 3 = 12

x = 12 → y = 15 - 12 = 3

Hence the 2 numbers are 3 and 12