int(2x-y+z)^(2)

int_(-1)^(1)int_(0)^(2)int_(x-2)^(x+2)(x+y+z)dxdydz

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))

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)-(y-z)^(2))/((x+z)^(2)-y^(2))+(y^(2)-(x-z)^(2))/((x+y)^(2)-z^(2))+(z^(2)-(x-y)^(2))/((y+z)^(2)-x^(2)) is -1(b)0(c)1(d) None of these

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

int_(z=0)^(1)int_(y=0)^(z)int_(x=0)^(y)xy^(2)z^(3)dxdydz is

(y^(2)+yz+z^(2))/((x-y)(x-z))+(z^(2)+zx+x^(2))/((y-z)(y-x))+(x^(2)+xy+y^(2))/((z-x)(z-y))