Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

minimized problem?

Given that a−b=24. If the product ab is minimized, what is the value of a^2+b^2?

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  • JOHN
    Lv 7
    4 weeks ago
    Favorite Answer

    ab = a(a – 24) = a² - 24a

    d(ab)/da = 2a – 24

    d²(ab)/da² = 2 > 0

    so ab has a minimum at 2a – 24 = 0 or at a = 12

    a – b = 24 → b = a – 24 = 12 -24 = -12.

    a² + b² = 12² + (-12)² = 144 + 144 = 288.

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  • 4 weeks ago

    Given that a − b = 24.

    If the product ab is minimized,

    the value of a^2 + b^2 = 626.

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  • a * b =>

    a * (24 + a)

    24a + a^2

    P = 24a + a^2

    dP/da = 24 + 2a

    dP/da = 0

    0 = 24 + 2a

    0 = 12 + a

    a = -12

    a - b = 24

    -12 - b = 24

    -12 - 24 = b

    -36 = b

    a^2 + b^2 =>

    (-12)^2 + (-36)^2 =>

    144 + 9 * 144 =>

    10 * 144 =>

    1440

    • atsuo
      Lv 6
      4 weeks agoReport

      You said b = 24+a , but if so then b-a = 24 . The question said a-b = 24 .

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