Question

If ab + bc + ca = 0, find the value of the equation in the above figure.

Answer 1

Put -ac = ab + bc ; -ab = ac+ bc and -bc =ab + ac
=(1/(a2+ab+ac))+(1/(c2+ac+bc))+(1/(a2+ab+ac))
=(1/a(a+b+c))+(1/b(a+b+c))+(1/c(a+b+c))
By taking LCM we get
=(ab + bc + ca)/[(a+b+c)(abc)]
put, ab+bc+ca=0
value = 0/[(a+b+c)(abc)] = 0