SOLUTION: If a,b,c, are in harmonic progression shown that (1/a+1/b-1/c)(1/b+1/c -1/a)=4/ac-3/b^2

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Question 974404: If a,b,c, are in harmonic progression shown that (1/a+1/b-1/c)(1/b+1/c -1/a)=4/ac-3/b^2
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If a,b,c, are in harmonic progression shown that (1/a+1/b-1/c)(1/b+1/c -1/a)=4/ac-3/b^2








The left side

%281%2Fa%2B1%2Fb-1%2Fc%29%281%2Fb%2B1%2Fc+-1%2Fa%29 becomes

%22%22=%22%22%28x-d%2Bx-x-d%29%28x%2Bx%2Bd-x%2Bd%29%29%22%22=%22%22%28x-2d%29%28x%2B2d%29%22%22=%22%22x%5E2-4d%5E2

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The right side:

4%2F%28ac%29%5E%22%22%22%22-%22%223%2Fb%5E2%22%22=%22%22

4%2A%281%2Fa%29%5E%22%22%2A%281%2Fc%29%5E%22%22%22%22-%22%223%2A%281%2Fb%29%5E2 becomes

4%2A%28x-d%29%2A%28x%2Bd%29-3%28x%29%5E2%22%22=%22%224%28x%5E2-d%5E2%29-3x%5E2%22%22=%22%224x%5E2-4d%5E2-3x%5E2%22%22=%22%22x%5E2-4d%5E2

Edwin