The numbers of integral solutions, ordered triplets `(x,y,z)` of `D=8`, where `D=|[y+z,z,y],[z,z+x,x],[y,x,x+y]|` is

|[y+z, x, y],[z+x, z, x],[x+y, y, z]|=...

|[z+y,x,x] , [y,z+x,y] , [z,z,x+y]|=

prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

The number of solutions to x+y+z=10 , where 1le x, y, z le 6 and x, y, z in N , is equal to

Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

If x+y+z=10 , where x,y,z in N . Find the number of solutions of triplet (x, y, z) such that no ttwo variables are equal.

Show that abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz

Let xyz=105 where x,y,z in N. Then number of ordered triplets (x,y,z) satisfying the given equation is