Give All Solutions of the Nonlinear System of Equations, Including $$x y = 11$$

question 471

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$x y = 11$$
$2 y ^ { 2 } - x ^ { 2 } = 11$

• A) \(\left\{ \left( \mathrm { i } \sqrt { 22 } , - \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , ( \sqrt { 11 } , \sqrt { 11 } ) \right\}\)
• B) \(\left\{ \left( - 22 , - \frac { 1 } { 2 } \right) , ( 11,1 ) \right\}\)
• C) \(\{ ( 2 \mathrm { i } \sqrt { 11 } , - \mathrm { i } \sqrt { 11 } ) , ( - 2 \mathrm { i } \sqrt { 11 } , \mathrm { i } \sqrt { 11 } ) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \}\)
• D) \(\left\{ \left( \mathrm { i } \sqrt { 22 } , - \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , \left( - \mathrm { i } \sqrt { 22 } , \frac { \mathrm { i } \sqrt { 22 } } { 2 } \right) , ( \sqrt { 11 } , \sqrt { 11 } ) , ( - \sqrt { 11 } , - \sqrt { 11 } ) \right\}\)

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