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Question

# Assertion :If a, b, c are three distinct positive number in H.P., then(a+b2aâˆ’b)+(c+b2câˆ’b)>4 Reason: Sum of any number and it's reciprocal is always greater than or equal to 2.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

## The correct option is C Assertion is correct but Reason is incorrectAssertion: 1b+1a2b−1a+1b+1c2b−1c=1b+1a1c+1b+1c1a =cb+ca+ab+ab=a+cb+(ca+ac)=(a+c)22ac+(ca+ac)=12(ac+ca+2)+(ca+ac)>4[∴x+1x>2 when x>≠1x]The reason is False as for this numbers should be positive.Assertion is correct but Reason is incorrect.

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