Final answer:
The student's math problem involves solving a complex equation with radicals. The solution requires simplifying the equation and potentially bringing it to a quadratic form, then using the quadratic formula by substituting the appropriate values for a, b, and c.
Step-by-step explanation:
The student is asked to solve the following equation: ²4x-16/³∙x-1 = 2. This is a mathematics problem involving radicals and possibly exponents. The given equation appears to be a bit complex due to the presence of different roots, but let's focus on the quadratic equations provided as examples in the reference information.
From the reference information, we see that a quadratic equation is typically of the form ax² + bx + c = 0. To solve such an equation, you can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a).
Applying the quadratic formula involves substituting the values of a, b, and c into the formula and then performing the arithmetic to find the values of x that satisfy the equation. Ensure you consider both the positive and negative solutions from the square root when using the formula.
The provided reference information demonstrates how the quadratic formula is used by plugging in different values for a, b, and c, such as a = 1, b = 0.0211, and c = -0.0211 or a = 3, b =13, c = -10. To find the correct answer in the context of the student's original question, one would need to simplify and manipulate the problem to reach a point where it resembles a quadratic equation, before then applying the relevant formula. For the given solutions in the examples, confirm whether they are applicable by checking the domain of the function (e.g., some roots cannot be negative).