For each equation, (b) solve for y in terms of x. See Example 8.
$2 x^{2} + 4 x y - 3 y^{2} = 2$

검증된 단계별 안내

Start with the given equation: $2x^{2} + 4xy - 3y^{2} = 2$.

Rewrite the equation to isolate terms involving $y$: $4xy - 3y^{2} = 2 - 2x^{2}$.

Recognize this as a quadratic equation in terms of $y$: $-3y^{2} + 4xy - (2 - 2x^{2}) = 0$.

Use the quadratic formula to solve for $y$, where $a = -3$, $b = 4x$, and $c = -(2 - 2x^{2})$. The formula is $y = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.

Substitute the values of $a$, $b$, and $c$ into the quadratic formula and simplify under the square root to express $y$ explicitly in terms of $x$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solving Quadratic Equations in Terms of One Variable

This involves isolating one variable (y) in an equation that may be quadratic in that variable. The goal is to express y explicitly as a function of x, often requiring rearrangement and use of the quadratic formula when y appears squared.

Quadratic Formula

The quadratic formula, y = [-b ± √(b² - 4ac)] / (2a), is used to solve quadratic equations of the form ay² + by + c = 0. Identifying coefficients a, b, and c correctly is essential to find the values of y in terms of x.

Algebraic Manipulation and Rearrangement

This concept involves rearranging terms, factoring, and simplifying expressions to isolate the desired variable. Careful manipulation is necessary to rewrite the equation in a standard quadratic form in y before applying the quadratic formula.

For each equation, (b) solve for y in terms of x. See Example 8. 2x2+4xy−3y2=22x^2 + 4xy - 3y^2 = 2