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# Test of Mathematics Solution Subjective 84 - Comparing Equations  This is a Test of Mathematics Solution Subjective 84 (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

Show that there is exactly one value of that satisfies the equation: ## Solution:

We know that for all    Now consider and . By AM-GM inequality we have, So , only when .

That means . So being the only solution.

and also satisfies Thus there is exactly one solution.

Hence Proved. This is a Test of Mathematics Solution Subjective 84 (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

Show that there is exactly one value of that satisfies the equation: ## Solution:

We know that for all    Now consider and . By AM-GM inequality we have, So , only when .

That means . So being the only solution.

and also satisfies Thus there is exactly one solution.

Hence Proved.

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