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2006 AMC 10B Problem 14

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2006 AMC 10B Problem 14AMC 10 Step by Step
Name:                             Date: September 13, 2026
Quadratics · difficulty 3 of 5 · about 3 min · position P11-15

Let aa and bb be the roots of the equation x2−mx+2=0x^2-mx+2=0 . Suppose that a+1ba+\frac1b and b+1ab+\frac1a are the roots of the equation x2−px+q=0x^2-px+q=0 . What is qq ?

  1. A)

    52\frac{5}{2}

  2. B)

    72\frac{7}{2}

  3. C)

    44

  4. D)

    92\frac{9}{2}

  5. E)

    88

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