If a2+b2,ab+bc and b2+c2 are in GP, prove that a,b,c are also in GP

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If a, b, c are in G.P., show that `a^(2) + b^(2), ab + bc` and `b^(2) + c^(2)` are also in G.P. If a, b, c are in G.P., show that `a^(2) + b^(2), ab + bc` and `b^(2) + c^(2)` are also in G.P.
If \( a, b, c \) are in G.P., prove that : are also in G.P. : \( a^{2}, b^{2}, c^{2} \) If \( a, b, c \) are in G.P., prove that : are also in G.P. : \( a^{2}, b^{2}, c^{2} \)
25. If a, b, c and d are in G.P. show that(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 . 25. If a, b, c and d are in G.P. show that(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .
If a, b, c are in GP, prove that `(a^(2)+b^(2)), (ab+bc), (b^(2)+c^(2))` are in GP. If a, b, c are in GP, prove that `(a^(2)+b^(2)), (ab+bc), (b^(2)+c^(2))` are in GP.
If `a, b, c` are in `G. P.`, prove that `a^2+ b^2, ab + bc, b^2 +c^2` are also in `G.P` If `a, b, c` are in `G. P.`, prove that `a^2+ b^2, ab + bc, b^2 +c^2` are also in `G.P`
If \( a, b, c \) are in G.P., prove that are also in G.P. : \( a^{3}, b^{3}, c^{3} \) If \( a, b, c \) are in G.P., prove that are also in G.P. : \( a^{3}, b^{3}, c^{3} \)
Suppose a, b, c are in A.P. and a2, b2, c2 are in G.P Suppose a, b, c are in A.P. and a2, b2, c2 are in G.P
If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 . a, b, c, d → ... If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 . a, b, c, d → ...