If `9(27)^(x^2+y+z)+9(27)^(x+y+z^2)+9(27)^(x+y^2+z)=11` then find the number of possible triplet `(x ,y ,z)dot`

If x, y, z are integers such that x >=0, y >=1, z >=2 and x + y + z = 15 , then the number of values of ordered triplets (x,y,z) are

If Z = x^2 - 7x - 9yi such that bar Z = y^2 i + 20i - 12 then the number of order pair (x,y) is :

If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3dot

Factorize: 1/(27)x^3-y^3+125 z^3+5x y z

Factorize: 27 x^3-y^3-z^3-9x y z

Find the angle between the planes -x+y+2z=9 and x+2y+z=5

The equation "cosec " x/2 + " cosec " y/2 + " cosec " z/2=6 , where 0 lt x, y,z lt pi/2 and x+y+z=pi , have i) Three Ordered triplet (x,y,z)solutions ii) Two ordered triplet (x,y,z) solutions. iii) Just one ordered triplet (x,y,z) solution iv) No ordered triplet (x,y,z) solution

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z y and (2) x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1). x y+y z+z y and (2). x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z x and (2) x(y+z)+y(z+x)+z(x+y)