Multiple Choice Question (MCQ)

If a+2b = 10, 2ab = 9, then |a-2b| =

  1. ×

    2

  2. ×

    4

  3. ×

    6

  4. 8

Collected in the board: Quadratic function

Steven Zheng posted 9 hours ago

Answer

  1. Given condition

    a+2b = 10
    (1)

    Square both sides of the equation

    (a+2b)^2 = 100

    Expand the LHS

    a^2+4b^2+2\cdot 2ab = 100

    then,

    a^2+4b^2 = 100-2\cdot 2ab = 100-2\cdot 9 = 82

    that is

    a^2+4b^2 =82
    (2)

    On the other hand, construct an equation using the conjugate of a+2b

    (a+2b)^2+(a-2b)^2 = 2(a^2+4b^2)
    (3)

    Substituting (1) and (2) results in

    (a-2b)^2 = 2\cdot 82-100=64

    Therefore

    |a-2b| = 8

    D is the correct option

Steven Zheng posted 9 hours ago

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