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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Definitions:

Compounded Monthly

A calculation method where interest is added to the principal sum at the end of each month, and future interest is calculated on the new total.

Future Value

Also known as the compound amount, the total value of an investment; equal to the principal plus all the compound interest.

Equal Amount

A quantity that is the same in size, number, or value when compared to another.

Compounded Quarterly

The process of calculating and adding interest to a principal sum four times a year, leading to compound growth in the interest amount.