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# Test of Mathematics Solution Subjective 81 - Cyclic and Symmetric Simultaneous Equations  This is a Test of Mathematics Solution Subjective 81 (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.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

## Problem

Find all possible real numbers which satisfy the following set of equations: ## Solution

Observing the symmetry and the cyclicity of the given set of equations it can be easily inferred that the real numbers and cannot be ordered i.e. one number cannot be greater or smaller than the other number else the system of equations will be inconsistent. This can be shown easily with the help of inequality.

Without loss of generality, we can say  that is greater or equal to them all, i.e., . Thus we have    As , we also have,    Thus we have Further calculations will show that is the only possible solution to this set of equations.

Thus we are left to solve just one equation, i.e., which gives Thus the possible values of the 5-tuple are:    This is a Test of Mathematics Solution Subjective 81 (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.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

## Problem

Find all possible real numbers which satisfy the following set of equations: ## Solution

Observing the symmetry and the cyclicity of the given set of equations it can be easily inferred that the real numbers and cannot be ordered i.e. one number cannot be greater or smaller than the other number else the system of equations will be inconsistent. This can be shown easily with the help of inequality.

Without loss of generality, we can say  that is greater or equal to them all, i.e., . Thus we have    As , we also have,    Thus we have Further calculations will show that is the only possible solution to this set of equations.

Thus we are left to solve just one equation, i.e., which gives Thus the possible values of the 5-tuple are:   ### Knowledge Partner  