Question

if ab+bc+ca=0 ,prove that a2b2+b2c2+c2a2=-2abc(a+b+c)​

Answer 1

Answer:

ab+bc+ca=0

squaring both side

(ab+bc+ca)^2=0

a^2b^2+b^2c^2+c^2a^2+2a^2bc+2ab^2c+2abc^2=0

a^2b^2+b^2c^2+c^2a^2+2abc(a+b+c)=0

a^2b^2+b^2c^2+c^2a^2=-2abc(a+b+c)

hence proved

Answer 2

Please find the attached image.