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9 February, 02:21

The sum of two numbers is 52. Their product is 100. What is the answer?

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Answers (2)
  1. 9 February, 02:32
    0
    {2, 52}

    Step-by-step explanation:

    Actually, there are two answers, not just one.

    Let the numbers be x and y.

    Then their sum is x + y and equals 52.

    Their product is xy and equals 100.

    We need to solve this system of equations for both x and y.

    Solving x + y = 52 for x, we get x = 52 - y.

    Substituting this result into the other equation, we get:

    (52 - y) y = 100

    This is a quadratic equation: 52y - y² = 100, or

    -y² + 52y - 100 = 0.

    Alternatively, y² - 52y + 100 = 0

    Let's solve this quadratic by "completing the square."

    First, identify the coefficient of the y term. It is - 52. Take half of that, obtaining - 26, square this result, obtaining 676. Add 676 to y² - 52y, and then subtract 676 from the result:

    y² - 52y + 676 - 676 + 100 = 0.

    Then (y - 26) ² = 576.

    Taking the square root of both sides, we get:

    y - 26 = ± 24, or:

    y = 24 + 26 = 50, and also:

    y = - 24 + 26 = 2

    Note that 2 (50) = 100, as it must, and that

    2 + 50 = 52 (also correct).

    The two-part answer is {2, 52}.
  2. 9 February, 05:30
    0
    Answer: 50,2

    Explanation:

    Let's call the two numbers a and b.

    The sum of them is 52 so a+b=52

    The product of them is 100 so ab=100

    We now have a system which we can solve in a variety of ways.

    My way:

    ab=100; b=100/a

    a+b=52; a + (100/a) = 52; (a^2/a) + (100/a) = 52; (a^2+100) / a=52

    a^2+100=52a

    a^2-52a+100=0

    This is now a quadratic which we can solve by factoring. We can use the factors - 50 and - 2

    Therefore, a^2-52a+100=

    (a-50) (a-2) or a equals 2 OR 50

    Therefore, b = (100/2) or b = (100/50) so b equals 50 OR 2 respectively.

    The answers are 50 and 2
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