Maths · Arithmetic and Geometric progressions
If and are in G.P. are in :
If \( a^{2}+b^{2}, a b+b c \) and \( b^{2}+c^{2} \) are in G.P. \( a, b, c \) are in :
- A. A.P.
- B. G.P.
- C. н.P.
- D. cannot be determined
Step-by-step solution
Given that a^2+b^2, ab+bc, and b^2+c^2 are in GP, we have (ab+bc)^2 = (a^2+b^2)(b^2+c^2). Expanding both sides and simplifying yields (ac - b^2)^2 = 0, so b^2 = ac, which implies a, b, c are in GP.
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