If real numbers $$ a,b, c $$ satisfy $$ a+b+c=0 $$ , $$ abc=4 $$ , which one best describes the value of $$ \dfrac{1}{a} +\dfrac{1}{b} +\dfrac{1}{c} $$

Question

If real numbers $$ a,b, c $$ satisfy $$ a+b+c=0 $$ , $$ abc=4 $$ , which one best describes the value of $$ \dfrac{1}{a}  +\dfrac{1}{b}  +\dfrac{1}{c}  $$

Uniteasy Admin · Accepted 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

$$ (a+b+c)^2 $$
$$ = a^2+ b^2+c^2+2(ab+bc+ac) $$

$$ 	herefore  ab+bc+ac=-\dfrac{a^2+b^2+c^2}{2} <0 $$

Multiple Choice Question (MCQ)

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