Given x, y, z are integers satisfying the equation `x^2+y^2+z^2=2xyz,` then find number of such triplets.

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 x,y,z are real numbers satisfying the equation 25(9x^2+y^2)+9z^2-15(5xy+yz+3zx)=0 then prove that x,y,z are in AP.

Find the number of triplets (x, y, z) of integers satisfying the equations x + y = 1 - z and x^(3) + y^(3) =1-z^(2) (where z ne 1 )

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

If x,y, z are real numbers satisfying the equation 25(9x^(2) + y^(2)) + 9z^(2)- 15 (5xy + yz + 3zx)= 0 then x,y, z are in

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

Let (x,y,z) be points with Integer coordinates satisfying the system of homogeneous equations 3x-y-z=0,-3x+2y+z=0,-3x+z=0.Then the number of such points for which x^2+y^2+z^2le100 is

If x,y,z are integers and x ge 0 , y ge 1 , z ge 2 , x+y+z = 15 , then the number of values of the ordered triplet (x,y,z) is :

If x, y, z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x, y, z) that satisfy the equation is

The equations x+y+z=6 x+2y+3z=10 x+2y+mz=n given infinite number of value of the triplet (x,y,z,) if