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Question

# If a, b, c are three distinct positive real numbers which are in H.P., then 3a+2b2aâˆ’b+3c+2b2câˆ’b is

A

Greater than or equal to 10

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B

Less than or equal to 10

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C

Only equal to 10

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D

None of these

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Solution

## The correct option is D None of these we have 1a,1b,1c are in A.P. Let 1a = p - q, 1b = p and 1c = p + q, where p,q > 0 and p > q. Now, substitute these values in 3a+2b2a−b+3c+2b2c−b then it reduces to 10+14q2p2−q2 which is obviously greater than 10(as p > q > 0). Trick: Put a = 1, b = 12, c = 13. The expression has the value 3+12−12+1+123−12 = 83+12>0

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