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

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}

×

Positive numbers
×

Zero
✓

Negative numbers
×

Positive or negative numbers

Steven Zheng posted 4 months ago

2
0
0

Answer

\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 posted 4 months ago