If a, b, c are in continued proportion, prove that
`(a+b+c)(a-b+c)=a^(2)+b^(2)+c^(2)`.

If a , b and c are in continued proportion, prove that : (i) (a^(2) + ab + b^(2))/(b^(2) + bc + c^(2)) = (a)/(c) (ii) (a^(2) + b^(2) + c^(2))/((a + b + c)^(2)) = (a - b + c)/(a + b + c) .

(i) If a , b , c are in continued proportion, show that : (a^(2) + b^(2))/(b(a+c)) = (b(a + c))/(b^(2) + c^(2)) . (ii) If a , b , c are in continued proportion and a(b - c) = 2b , prove that : a - c = (2(a + b))/(a) . (iii) If (a)/(b) = (c)/(d) show that : (a^(3)c + ac^(3))/(b^(3)d +bd^(3)) = ((a + c)^(4))/((b + d)^(4)) .

if (a^(2) + c^(2)) , (ab + cd) and (b^(2) + d^(2)) are in continued proportion, prove that a , b , c and d are in proportion.

If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4 .

If a ,\ b ,\ c are in proportion, then (a) a^2=b c (b) b^2=a c (c) c^2=a b (d) None of these

If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c+c a)

If a ,b,c , d are in G.P. prove that (a-d)^(2) = (b -c)^(2)+(c-a)^(2) + (d-b)^(2)

If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)

If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

If a ,b ,c are in G.P., prove that: a(b^2+c^2)=c(a^2+b^2)