If `a , b , c ,` are in `A P ,a^2,b^2,c^2` are in HP, then prove that either `a=b=c` or `a , b ,-c/2` from a GP (2003, 4M)

If a ,b ,c are in A.P. and a^2, b^2, c^2 are in H.P., then prove that either a=b=cora ,b ,-c/2 form a G.P.

If a,b,c, are in AP,quad a^(2),b^(2),c^(2) are in HP ,then prove that either a=b=c or a,b,-(c)/(2) from a GP (2003,4M)

If A=2B , then prove that either c=b or a^2 = b(c+b)

If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

If A=2B, then prove that either c=b or a^(2)=b(c+b)

If a, b, c are in A.P. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

If a,b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P. then prove that either a^(2),b^(2),c^(2) are in H.P.a=b=c or a,b,-(c)/(2) form a G.P.

If a, b, c are in GP, prove that a^(2), b^(2), c^(2) are in GP.

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.