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Question

If ab + c2; a - b + c = b + c ; 1, then prove that b is the geometric mean between a and c.

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Solution

ab+c2a-b+c=b+c1 (Given)By cross-multiplying, we get: ab+c2=b+ca-b+cab+c2=ab-b2+bc+ac-bc+c2b2=acTherefore, b is the geometric mean between a and c.

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