Question

Using properties of determinants prove that: |(1,b + c,b² + c²),(1,c + a, c² + a²),(1,a + b,a² + b²) = (a - b)(b - c)(c - a)

Answer 1

Considering LHS

It can be written as

= (a - b)(b - c)(c + b - b - a)

So we get

= (a - b)(b - c)(c - a) = RHS

Hence, it is proved.