Add:` `2x(z-x-y)`and `2y(z-y-x)`

Solve the following system of equations by matrix method: x+y+z=6,x-y-z=-4 and x+2y-2z=-1 .

If (x(y+z-x))/log x = (y(z+x-y))/log y = (z(x+y-z))/log z ," prove that "x^(y) y^(x) = z^(y) y^(z) = x^(z) z^(x) .

Verify that : x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2] Consider R.H.S

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

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

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

Add: x^2-y^2-1,y^2-1-x^2,1-x^2-y^2