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 prove that a^4+b^4+c^4=1/2(a^2+b^2+c^2)^2

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

If a+b+c=0 , then prove that a^4+b^4+c^4=2(ab+bc+ca)^2

If a + b + c = 0 , prove that a^(4) + b^(4) + c^(4) = 2(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) = 1//2 (a^(2) + b^(2) + c^(2))^(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)

Prove that If a=2, b=3, c=5. Then prove that 2b^2c^2+2c^2a^2+2a^2b^2-a^4-b^4-c^4=0

If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

If a+b+c=0 then prove the following. a^(4) +b^(4) +c^(4) =2(b^(2)c^(2) +c^(2)a^(2) +a^(2)b^(2)) =(1)/(2) (a^(2)+b^(2)+c^(2))^(2)