IF a+b+c=0 then
`(a^2+b^2+c^2)/((a-b)^2+(b-c)^2+(c-a)^2)`=

If a + b + c = 0 , then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-c^2-a^2)+(2c^2)/(c^2-a^2-b^2)=3

If a+b+c=0 prove that (a^4+b^4+c^4)/(a^2b^2+b^2c^2+c^2a^2)=2

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .

If a/b =b/c and a,b, c gt 0 , then prove that (a+b)^2/(b+c)^2 = (a^2 +b^2)/(b^2 +c^2)

If a+b+c=0 , find the value of (a^2)/((a^2-b c))+(b^2)/((b^2-c a))+(c^2)/((c^2-a b)) (a) 0 (b) 1 (c) 2 (d) 4

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.