if x,y,z are in GP then prove that:
px+y x y
py+z y z = 0
0 px+y py+z

x, y, z are in GP so, y2=xz....1Now taking LHS, px+yxypy+zyz0px+ypy+zNow expanding along R1 we get, =px+ypy2+yz-pzx-yz-xp2y2+z2+2pyz+yp2xy+py2+pxz+yz=px+ypxz+yz-pzx-yz-xp2y2+z2+2pyz+yp2xy+pxz+pxz+yz using equation1=0-xp2y2-xz2-2pxyz+xp2y2+2pxyz+y2z=-xz2+xz2  using equation1=0

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