If a-b-c-0- then 1-b2-c2-z2-1-c2-a2-b2-1-a2-b2-c2 is equal to -

A+b+c = 0 1/a^2+b^2 c^2+1/b^2+c^2 a^2+1/c^2+a^2 b^2 =1/(a+b)^2 2ab c^2+1/(b+c)^2 2bc a^2+1/(c+a)^2 2ca b^2 =1/( c)^2 2ab c^2+1/( a)^2 2bc a^2+1/( b)^2 2ca b^2 ...

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Standard X

Mathematics

Rational Expression

If a+b+c=0, t...

Question

If $a + b + c = 0, t h e n (\frac{1}{b^{2} + c^{2} - a^{2}}) + (\frac{1}{c^{2} + a^{2} - b^{2}}) + (\frac{1}{a^{2} + b^{2} - c^{2}})$ is equal to :

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Solution

a+b+c = 0
$\frac{1}{a^{2} + b^{2} - c^{2}} + \frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} = \frac{1}{(a + b)^{2} - 2 a b - c^{2}} + \frac{1}{(b + c)^{2} - 2 b c - a^{2}} + \frac{1}{(c + a)^{2} - 2 c a - b^{2}} = \frac{1}{(- c)^{2} - 2 a b - c^{2}} + \frac{1}{(- a)^{2} - 2 b c - a^{2}} + \frac{1}{(- b)^{2} - 2 c a - b^{2}} = - \frac{1}{2} \frac{c + b + a}{a b c} = 0$

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If a+b+c=0,then(1b2+c2−a2)+(1c2+a2−b2)+(1a2+b2−c2) is equal to :

a+b+c = 0 1a2+b2−c2+1b2+c2−a2+1c2+a2−b2=1(a+b)2−2ab−c2+1(b+c)2−2bc−a2+1(c+a)2−2ca−b2=1(−c)2−2ab−c2+1(−a)2−2bc−a2+1(−b)2−2ca−b2=−12c+b+aabc=0

If $a + b + c = 0, t h e n (\frac{1}{b^{2} + c^{2} - a^{2}}) + (\frac{1}{c^{2} + a^{2} - b^{2}}) + (\frac{1}{a^{2} + b^{2} - c^{2}})$ is equal to :