Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations 3 x-y-z=0,-3 x+z=0,-3 x+2 y+z=0 . Then, the number of such points for which x^2+y^2+z^2 100 is

Step-by-step solution

Given, 3 x-y-z=0 and array r -3 x+2 y+z=0 -3 x+z=0 array On adding Eqs. (i) and (ii), we get y=0 So, 3 x=z Now, x^2+y^2+z^2 100 array lc & x^2+(3 x)^2+0 100 & 10 x^2 100 & x^2 10 & x=-3,-2,-1,0,1,2,3 array So, number of such 7 points are possible.