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प्रश्न
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
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उत्तर
Since a, b, c, d are in G.P.
Again A.M. > G.M. for the first three terms
`(a + c)/2 > b` .....`("Since" sqrt(ac) = b)`
⇒ a + c > 2b ....(3)
Similarly, for the last three terms
`(b + d)/2 > c` .....`("Since" sqrt(bd) = c)`
⇒ b + d > 2c ....(4)
Adding (3) and (4), we get
(a + c) + (b + d) > 2b + 2c
a + d > b + c
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