गुणनखण्ड कीजिए : `(x-y+z)^(2)+(y-z+x)^(2)+2(x-y+z)(y+z+x)`.

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........

If (x+ y-z -1)^(2) + (z+ x-y - 2)^(2) + (z+y-x-4)^(2)=0 find x+ y+z =?

If (x+y-z)^(2) +(y+z-x)^(2) +(z+x-y)^(2)=0 then what is the value of x+y+z ?

If x + y = 2z then (x)/(x-z) +(z)/(y-z) = ?

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

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))

"The value of "(x^(2))/((x-y)(x-z))+(y^(2))/((y-z)(y-x))+(z^(2))/((z-x)(z-y))" is : "