Question

∛(2x+1)+∛(2x+2)+∛(2x+3)=0

Answer 1

Рассмотрим функцию $f(x)=\sqrt[3]{2x+1}+\sqrt[3]{2x+2}+\sqrt[3]{2x+3}$. Эта функция является возрастающей на всей числовой оси (как сумма трёх возрастающих функций). График функции $f(x)$ с прямой $y=0$ имеет одно пересечение, т.е. уравнение имеет единственное решение, путём подбора находим $x=-1.$

Ответ: x = -1.

Answer 2

The equation you've provided is a cubic equation involving three cube roots. To solve for the value of 'x', you need to isolate the variable on one side of the equation. Unfortunately, cubic equations like this one do not have a general algebraic solution that can be expressed in terms of elementary functions. Instead, you typically solve these equations numerically or graphically.

If you have access to a graphing calculator or a computer algebra system, you can plot the graph of the function $f(x) = \sqrt[3]{2x+1} + \sqrt[3]{2x+2} + \sqrt[3]{2x+3}$ and find the x-values where the graph intersects the x-axis (i.e., where $f(x) = 0$). This will give you approximate solutions.

If you're looking for a more precise numerical solution, you might use iterative numerical methods such as the Newton-Raphson method or the bisection method to find the roots of the equation.

If you provide a specific value or range for 'x' that you're interested in, I can help you approximate a solution using numerical methods.