Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { r } 5 x ^ { 2 } + 3 x y - 5 y ^ { 2 } = - 9 \\x ^ { 2 } - x y - y ^ { 2 } = - 5\end{array}$

question 500

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { r } 5 x ^ { 2 } + 3 x y - 5 y ^ { 2 } = - 9 \\x ^ { 2 } - x y - y ^ { 2 } = - 5\end{array}$

• A) \(\left\{ ( - 1 , - 2 ) , ( 1,2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}\)
• B) \(\{ ( - 1,2 ) , ( 1 , - 2 ) , ( 2 \mathrm { i } , \mathrm { i } ) , ( - 2 \mathrm { i } , - \mathrm { i } ) \}\)
• C) \(\{ ( - 1 , - 2 ) , ( 1,2 ) , ( 2 i , - i ) , ( - 2 i , i ) \}\)
• D) \(\left\{ ( - 1,2 ) , ( 1 , - 2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}\)

Identify the characteristics and consequences of authoritarian personalities.

Understand the principles of social influence, including reciprocity, social facilitation, and social loafing.

Examine the dynamics and effects of group behavior on decision-making, including groupthink and group polarization.

Explore the concept of deindividuation in crowd behavior and its effect on individual actions.

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Definitions:

Mean

The mean is a measure of central tendency that is calculated by adding up all values in a dataset and dividing by the number of values.

Variance

The statistical measurement of the spread between numbers in a data set, indicating how much the elements differ from the mean.

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