Question

Using properties of determinants prove that: |(x,y,z),(x²,y²,z²),(x³,y³,z³)| = xyz(x - y)(y - z)(z - x)

Answer 1

We know that

So we get

On further calculation

= xyz(x – y) (y – z) (y + z – x – y)

So we get

= xyz(x – y) (y – z) (z – x)

= RHS

Hence, it is proved.