Give All Solutions of the Nonlinear System of Equations, Including $$x ^ { 2 } + 3 x y + y ^ { 2 } = 4$$

question 381

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$x ^ { 2 } + 3 x y + y ^ { 2 } = 4$$
$x ^ { 2 } - 3 x y - y ^ { 2 } = 4$

• A) \(\{ ( 2,0 ) , ( - 2,0 ) , ( 2 , - 6 ) , ( - 2,6 ) \}\)
• B) \(\{ ( 2,0 ) , ( - 2,0 ) \}\)
• C) \(\{ ( 0,2 ) , ( 0 , - 2 ) , ( 2 , - 6 ) , ( - 2,6 ) \}\)
• D) \(\{ ( 2 , - 6 ) , ( - 2,6 ) \}\)

---

Definitions:

Schizophrenia

A chronic and severe mental disorder that affects how a person thinks, feels, and behaves, often characterized by delusions, hallucinations, and impaired functioning.

Positive Symptom

Symptoms that add abnormal thoughts, behaviors, or perceptions, such as hallucinations or delusions, especially relevant in discussing psychotic disorders.

Motor Difficulties

Challenges or impairments in the ability to perform movements or tasks that require motor coordination.

Schizophrenogenic Mother

A controversial and largely discredited theory suggesting a cold, domineering, and conflicting maternal style could contribute to the development of schizophrenia in children.