Question

if ab+bc+ca=0,prove that 1/a^2-bc + 1/b^2-ca +1/c^2-ab=0

Answer 1

ab+bc+ca=0

1/a^2 - bc + 1/ b^2 -ca+1/c^3 -ab = 0

Let -bc= ab +ca

- ca= ab+bc

-ab= ac+bc

1/(a^2+ab+ca )+ 1/(b^2+ab+bc)+1/(c^2+ac+bc)

1/a(a+b+c) +1/b(b+a+c) + 1/c(c+a+b)

Taking LCM

bc+ac+ab/abc(a+b+c)

It's given ab+bc+ca = 0

0/abc(a+b+c) = 0

H.T.P