Answer:
3 and 12
Step-by-step 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
