If a , b , c are in AP and A.G are arithmetic and geometric mean , between a and b while $\;A^{|}\;and\;G^{|}$ are A.M and G.M between B and C . then

Question

$(a)\;A^2+G^2={A^{|}}^{2}+{G^{|}}^{2}\qquad(b)\;A^2-G^2={A^{|}}^{2}-{G^{|}}^{2}\qquad(c)\;A^2+{A^{|}}^{2}=G^2+{G^{|}}^{2}\qquad(d)\;{A^{|}}^{2}+A^2={G^{|}}^{2}-G^2$