17.x(x+y-z)-yz

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

If matrix A=[02 y z x y-zx-yz] satisfies AT = A-1, then find the value of x, y, z.

tan ^ (- 1) ((sqrt (x (x + y + z))) / (yz)) + tan ^ (- 1) sqrt ((y (x + y + z)) / (xz)) + tan ^ (- 1) (sqrt ((z (x + y + z)) / (xy))) = pi

Three variable x,y,z such that y+z-x is a constant and if (z+x-y)(x+y-z) alpha yz, then show that (x+y+z) alpha yz .

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .