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

question 97

Multiple Choice

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

• A) \(\{ ( 1,0 ) \}\)
• B) \(\{ ( 1,0 ) , ( - 1,0 ) , ( 0,1 ) , ( 0 , - 1 ) \}\)
• C) \(\{ ( 1,0 ) , ( - 1,0 ) \}\)
• D) \(\{ ( 1,0 ) , ( 0,1 ) \}\)

Understand the significance of asset allocation in achieving high total returns.

Comprehend the importance of investment companies in financial planning and achieving long-term goals.

Grasp the reasons behind the demographic distribution of mutual fund ownership.

Explain the processes involved in purchasing, managing, and withdrawing from mutual funds.

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Definitions:

\(8 !\)

The factorial of 8, which is the product of all positive integers less than or equal to 8, calculated as \(8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).

\(11 !\)

Denotes the factorial of 11, which is the product of all positive integers from 1 to 11, calculated as \(11! = 11 \times 10 \times 9 \times ... \times 1\).

\(6 ^ { n + 2 }\)

An exponential expression representing six raised to the power of n plus two, where n is any real number.

\(- 1\)

Represents a negative unit value in mathematics, often used to indicate the opposite or additive inverse of a positive value.