If a+b+c=0, find b2+c2+a2/b2-ca - Maths -

Question

If a+b+c=0, find
b2+c2+a2/b2-ca

Gursheen kaur. · Accepted Answer

Given: a+b+c= 0 (i) $S q u a r i n g b o t h s i d e s, w e g e t, {(a + b + c)}^{2} = 0 \Rightarrow a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a = 0 \Rightarrow a^{2} + b^{2} + c^{2} = - 2 (a b + b c + c a)$ If a+b+c= 0[Given] then b= -c-a Squaring both sides, we get, $b^{2} = c^{2} + a^{2} + 2 c a$ $N o w, t h e v a l u e o f \frac{b^{2} + c^{2} + a^{2}}{b^{2} - c a} = \frac{- 2 (a b + b c + c a)}{c^{2} + a^{2} + 2 c a - c a} = \frac{- 2 (a b + b c + c a)}{c^{2} + a^{2} + c a}$