If `a ,b ,c` are in G.P., prove that: 1) `a(b^2+c^2)=c(a^2+b^2)` , 2) `A^2b^2c^2(1/(a^3)+1/(b^3)+1/(c^3))=a^3+b^3+c^3` , 3) `((a+b+c)^2)/(a^2+b^2+c^2)=(a+b+c)/(a-b+c)` , 4)`1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)` ,5) (a+2b=2c)(a-2b+2c)`=a^2+4c^2dot`