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

question 64

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

---

Definitions:

β-D-Glucopyranose

A chemical structure of glucose in its cyclic form, where the glucose molecule forms a six-membered ring, with the hydroxyl group on the first carbon in the beta configuration.

α-D-Ribofuranose

A sugar derivative where the pentose sugar ribose is in its furanose form (a five-membered oxygen-containing ring) and has a specific orientation (alpha) of the hydroxyl group attached to the anomeric carbon.

Epimers

Stereoisomers that differ in configuration at only one stereogenic center among several.

D-Arabinose

A naturally occurring pentose sugar, which is a component of many polysaccharides and glycoproteins.