Solve the Equation for the Indicated Variable $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$

question 394

Multiple Choice

Solve the equation for the indicated variable. Assume no denominator is 0.
- $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$ , for $y$

• A) \(y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }\)
• B) \(y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }\)
• C) \(y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }\)
• D) \(y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }\)

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Definitions:

Regression Analysis

A statistical method for estimating the relationships among variables, typically one dependent variable and one or more independent variables.

Categorical Data

Data that can be sorted into categories based on qualitative properties or attributes, such as names or labels.

Numerical Data

Information that can be measured or counted and represented in numbers and values.

Multicollinearity

A statistical phenomenon in which two or more independent variables in a regression model are highly correlated, potentially distorting the results.