![]() Therefore, the solutions to the equation 3x^(2/3) - 5x^(1/3) + 2 = 0 are x = 8/27 and x = 1. When y = 1, x^(1/3) = 1, which results in x = 1. To find the solutions for x, we substitute y back into the equation. Solving for y gives us two solutions: y = 2/3 and y = 1. Using factorization, we find the factors as (3y - 2)(y - 1) = 0. To simplify it, we can let y = x^(1/3).īy substituting y into the equation, we obtain 3y^2 - 5y + 2 = 0, which is a quadratic equation. Notice that this equation involves fractional exponents. Now, let's move on to another complex quadratic equation: 3x^(2/3) - 5x^(1/3) + 2 = 0. ![]() For y = 4, we have x^2 = 4, yielding two solutions: x = 2 and x = -2. As We Are solving for x, we substitute y back into the equation.įor y = 1/4, we have x^2 = 1/4, which gives us two solutions: x = 1/2 and x = -1/2. By solving for y, we obtain two possible values: y = 1/4 and y = 4. In this case, the factors are (4y - 1)(y - 4) = 0. To find the solutions, we can factorize the quadratic equation. By substituting y = x^2, the equation becomes 4y^2 - 17y + 4 = 0, which is a quadratic equation. To simplify it, we can rewrite 4x^4 as (4x^2)^2. This equation has a degree of x^4, making it complex to solve directly. To understand the transformation process, let's consider the equation 4x^4 - 17x^2 + 4 = 0. By substituting a suitable variable, we can simplify the equation and proceed with the solution. The transformation can be done through various techniques, such as substitution. When faced with complex quadratic equations, it is essential to know how to transform them into a simpler quadratic form. This article aims to guide You through the process of solving complex quadratic equations by providing step-by-step examples and explanations. While solving simple quadratic equations may be straightforward, dealing with complex quadratic equations requires more advanced techniques and methods. In mathematics, quadratic equations play a crucial role in various problem-solving scenarios. 2.1 Transforming Equations into Quadratic Equations
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