[" 2.सरल कीजिए: "],[[" (i) "(x+y+z)^(2)+(x-y+z)^(2)+(x+y-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))

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))

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

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

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

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= ........

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

Show that Delta=|[(y+z)^2, x y , z x],[ x y, (x+z)^2, y z],[ x z, y z, (x+y)^2]|=2 x y z(x+y+z)^3