Show that `Delta=|(y+z)^2x y z xx y(x+z)^2y z x z y z(x+y)^2|=2x y z(x+y+z)^3`.

Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

2x + 3y + z = 11, x + 2y + z = 8, x-y + z = 2

A person travels three equal distances at a speed of x km/hr, y km/hr and z knyhr respectively. What is the average speed for the whole journey? (x y z)/(3(x y+y z+z x)) b. (x y z)/((x y+y z+z x)) c. ((x y+y z+z x))/(x y z) d. (3x y z)/((x y+y z+z x))

Prove that |[x+y, y+z, z+x] , [z+x, x+y, y+z] , [y+z, z+x, x+y]|=2|[x,y,z] , [z,x,y] , [y,z,x]|

Add 2x - 3y + z , 5y - x + 7z and 3x - y - 6z.

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x