if a, b , c are in GP. prove that a2 + b2, ab+ bc, b2 + c2are also in GP Share with your friends Share 6 Devesh Kumar answered this As we are given a, b,c are in G.P lets assume, a=br; b=b; c=brWhere r→common ratio between the terms such that ratio of cb=baNow, we calculate value of a2 + b2, ab+ bc, b2 + c2 to prove that these are in G.P1st term=a2 + b2=br2+b2=b21+r2r22nd term ab+ bc=br×b+b×br=b21+r2r3rd term b2 + c2=b2+b2r2=b21+r23rd term2nd term=b21+r2b21+r2r=b21+r2×rb21+r2=r …12nd term1st term=b21+r2r×r2b21+r2=r …2From eq 1 & 2common ratios are same so a2 + b2, ab+ bc, b2 + c2 in G.P Answer 18 View Full Answer Akash answered this Nice question. I solved it and got a part of ab+bc =a+c. it may solve further... 7 Akash answered this as upper answer is mine next you should use b^2=a×c. then from this u can prove (a+c)^2=(b^2+c^2)(a^2+c^2)and put value of a+c and make in simple form of ba=cb. so here comes a,b,c are in gp as b^2 =a×c 2
