Number of points common to the spheres x2+y2+z2=36 and x2+y2+z2−20x+84=0 is

For sphere x2+y2+z2=36 centre is C1(0,0,0) and radius is r1 = 6. For sphere x2+y2+z2−20x+84=0 centre is  C2(10,0,0) and radius is r2 = 6. C1C2=10 and r1+r2=6+4=10Thus, two spheres touch externally at point (6, 0, 0).