SOLUTION: if a,b,c are in AP, aalnd a,mb,c are in GP then a, m^2b, c are in HP

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Question 1091492: if a,b,c are in AP, aalnd a,mb,c are in GP then a, m^2b, c are in HP
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if a,b,c are in AP, and a,mb,c are in GP then a, m%5E2b, c are in HP+
a,b,c are in AP hence 2b+=+a%2Bc -------------(1)
a,mb,c are in GP hence m%5E2b%5E2+=+ac ---------------(2)
divide (2) by (1)
%28m%5E2b%5E2%29%2F2b+=+ac%2F%28a%2Bc%29
%28m%5E2b%29%2F2+=+ac%2F%28a%2Bc%29
%28m%5E2b%29%28a%2Bc%29+=+2ac
%28a%2Bc%29%2Fac+=+2%2F%28m%5E2b%29
2%2F%28m%5E2b%29=+1%2Fa+%2B+1%2Fc
hence a, m%5E2b, c are in HP+