If a, b, c are rational numbers but not zero, $$ a+b+c=0 $$ , what is the value of
$$ \dfrac{1}{b^2+c^2-a^2} +\dfrac{1}{c^2+a^2-b^2} +\dfrac{1}{a^2+b^2-c^2} $$

Question

If a, b, c are rational numbers but not zero, $$ a+b+c=0 $$ , what is the value of 
$$ \dfrac{1}{b^2+c^2-a^2}  +\dfrac{1}{c^2+a^2-b^2}  +\dfrac{1}{a^2+b^2-c^2}  $$

Uniteasy Admin · Accepted Answer

$$ \because  a+b+c=0 $$
$$ 	herefore   (a+b)^2=c^2 $$
$$ 	herefore  a^2+b^2-c^2=2ab $$

Similarly,

$$ b^2+c^2-a^2=2bc $$
$$ a^2+c^2-a^2=2ac $$

$$ \dfrac{1}{b^2+c^2-a^2}  +\dfrac{1}{c^2+a^2-b^2}  +\dfrac{1}{a^2+b^2-c^2}   $$

$$ =\dfrac{1}{2ab}  +\dfrac{1}{2bc}  +\dfrac{1}{2ab}  $$
$$ =\dfrac{a+b+c}{2abc }  $$
$$ =0 $$

Multiple Choice Question (MCQ)

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