Between any two nonzero real numbers a,b, insert one arithmetic mean A and two geometric means p,q, so a,A,b form an A.P. and a,p,q,b form a G.P. Statement 1: p 3 + q 3 = 2 Apq. Statement 2: If x,y,z

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Between any two nonzero real numbers a,b, insert one arithmetic mean A and two geometric means p,q, so a,A,b form an A.P. and a,p,q,b form a G.P. Statement 1: p 3 + q 3 = 2 Apq. Statement 2: If x,y,z form a G.P., then y 2 = xz .

TestHub · Accepted Answer

Statement 2 applied to a,p,q and p,q,b gives p²=aq and q²=pb. Multiplying by p and q gives p³=apq and q³=bpq. Adding gives p³+q³=(a+b)pq=2Apq, since A=(a+b)/2. Both statements are true, and Statement 2 explains Statement 1.

Mathematics - Sequence & Series Question with Solution | TestHub

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