Selective Question

If real numbers a,b, c satisfy a+b+c=0 , abc=4 , which one best describes the value of

\dfrac{1}{a} +\dfrac{1}{b} +\dfrac{1}{c}

  1. ×

    Positive numbers

  2. ×

    Zero

  3. ✓

    Negative numbers

  4. ×

    Positive or negative numbers

Steven Zheng Steven Zheng posted 3 weeks ago


Answer

  1. \dfrac{1}{a} +\dfrac{1}{b} +\dfrac{1}{c}

    =\dfrac{ab+bc+ac}{abc}

    =\dfrac{ab+bc+ac}{4}

    \because a+b+c=0

    \quad and

    (a+b+c)^2

    = a^2+ b^2+c^2+2(ab+bc+ac)

    \therefore ab+bc+ac=-\dfrac{a^2+b^2+c^2}{2} <0

Steven Zheng Steven Zheng posted 3 weeks ago


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