?If for a binary solution one starts with an expression for M (or \(M^{R} \text { or }

Chapter 10, Problem 10.11

(choose chapter or problem)

If for a binary solution one starts with an expression for M (or \(M^{R} \text { or } M^{E}\)) as a function of \(x_{1}\) and applies Eqs. (10.15) and (10.16) to find \(\bar{M}_{1} \text { and } \bar{M}_{2}\) (or \(\bar{M}_{1}^{R} \text { and } \bar{M}_{2}^{R} \text { or } \bar{M}_{1}^{E} \text { and } \bar{M}_{2}^{E}\)) and then combines these expressions by Eq. (10.11), the initial expression for M is regenerated. On the other hand, if one starts with expressions for M¯ 1 and M¯ 2 , combines them in accord with Eq. (10.11), and then applies Eqs. (10.15) and (10.16), the initial expressions for \(\bar{M}_{1} \text { and } \bar{M}_{2}\) are regenerated if and only if the initial expressions for these quantities meet a specific condition. What is the condition?

Text Transcription:

M^R or M^E

x_1

barM_1 and barM_2

barM_1^R and barM_2^R or barM_1^E and barM_2^E