Question Number 10245 by j.masanja06@gmail.com last updated on 31/Jan/17

prove that    determinant ((1,1,1),(x,y,z),(x^2 ,y^2 ,z^2 ))=(x−y)(y−z)(z−y)

Answered by prakash jain last updated on 31/Jan/17

 determinant ((1,1,1),(x,y,z),(x^2 ,y^2 ,z^2 ))    C1−C2→C1, C2−C3→C2   determinant ((0,0,1),((x−y),(y−z),z),((x^2 −y^2 ),(y^2 −z^2 ),z^2 ))     determinant ((0,0,1),((x−y),(y−z),z),(((x−y)(x+y)),((y−z)(y+z)),z^2 ))    (x−y)(y−z) determinant ((0,0,1),(1,1,z),(((x+y)),((y+z)),z^2 ))    Expanding wrt row 1  (x−y)(y−z)((y+z)−(x+y))  =(x−y)(y−z)(z−x)