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Question
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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Solution
Since a, b, c, d are in A.P.
Then A.M. > G.M.
For the first three terms.
Therefore, `b > sqrt(ac) ("Here" (a + c)/2 = b)`
Squaring, we get
b2 > ac ....(1)
Similarly, for the last three terms
A.M. > G.M.
`c > sqrt(bd) ("Here" (b + d)/2 = c)`
c2 > bd ....(2)
Multiplying (1) and (2), we get
b2 c2 > (ac) (bd)
⇒ bc > ad
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