Question

If a+b+c=0 firnd the value of (a+b) 2 /ab+(b+c) 2 /bc+(c+a) 2 /ca

Answer 1

(a+b)²/ab + (b+c)²/bc + (c+a)²/ca
= (–c)²/ab + (–a)²/bc + (–b)²/ca
= c²/ab + a²/bc + b²/ca
= (a³+b³+c³) / abc
= [(a+b+c) (a²+b²+c²–ab–bc–ca)+3abc] / abc
= (0×(a²+b²+c²–ab–bc–ca)+3abc) / abc
= 3abc / abc
= 3