This is a Test of Mathematics Solution Subjective 78 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

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For real numbers , and , show that

.

Applying Ravi transformation

, and .

Our inequality reduces to .

.

Now we know, .

Applying this we get

L.H.S =

=

= R.H.S **(proved)**