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# Test of Mathematics Solution Subjective 83 - Two numbers adding up to 1  This is a Test of Mathematics Solution Subjective 83 (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.

## Problem

If a and b are positive real numbers such that a + b = 1, prove that + ## Solution:

We replace 1 by a+b and expand the squares.   Now we use A.M. - G.M. inequality to have  Also we apply the square mean inequality to have Since a+b = 1, we have Combining all of them we have Discussion

Some theoretical background. This is a Test of Mathematics Solution Subjective 83 (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.

## Problem

If a and b are positive real numbers such that a + b = 1, prove that + ## Solution:

We replace 1 by a+b and expand the squares.   Now we use A.M. - G.M. inequality to have  Also we apply the square mean inequality to have Since a+b = 1, we have Combining all of them we have Discussion

Some theoretical background.

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