Solve this:

Q(iii) If x_1, x₂ be the roots of the equation $\mathrm{A}\left({\mathrm{x}}^2 + {\mathrm{m}}^2\right) + \mathrm{Amx} + {\mathrm{Bm}}^2{\mathrm{x}}^2 = 0 \mathrm{then} \mathrm{prove} \mathrm{that} \mathrm{A} \left({\mathrm{x}}_3^2 + {\mathrm{x}}_2^2\right) +\mathrm{A} {\mathrm{x}}_1{\mathrm{x}}_2 + {\mathrm{Bx}}_1^2{\mathrm{x}}_2^2 = 0$

  (iv) Prove that the two equations x² – 2ax + b² = 0 and x² – 2bx + a² = 0 are such that the A.M. of the roots of the one is equal to the G.M. of the roots of other.