Determine the Real Solutions to the System of Nonlinear Equations $$\begin{array} { l } x ^ { 2 } - 3 y ^ { 2 } = 1 \\2 x ^ { 2 } + 3 y ^ { 2 } = 47\end{array}$$

question 129

Multiple Choice

Determine the real solutions to the system of nonlinear equations.
- $$\begin{array} { l } x ^ { 2 } - 3 y ^ { 2 } = 1 \\2 x ^ { 2 } + 3 y ^ { 2 } = 47\end{array}$$

• A) \(( 4,5 ) , ( - 4 , - 5 )\)
• B) \(( 5,4 ) , ( - 5 , - 4 )\)
• C) \(( 4,5 ) , ( - 4,5 ) , ( 4 , - 5 ) , ( - 4 , - 5 )\)
• D) \(( 5,4 ) , ( - 5,4 ) , ( 5 , - 4 ) , ( - 5 , - 4 )\)

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Definitions:

Optimal

The best or most favorable point, level, or condition, especially under specific constraints or conditions.

Maximin Strategy

A decision rule which aims to maximize the minimum payoff attainable, often used under conditions of uncertainty.

Payoffs

The returns or benefits received from a particular action or investment.

Nash Equilibrium

A concept within game theory where each player's strategy is optimal, given the strategies of other players, and no player has anything to gain by changing their own strategy alone.