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1 August, 14:40

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

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  1. 1 August, 14:46
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    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
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