Question

6arcctg(3x^2+x+√3)=π Решите пожалуйста. Совсем запуталась

Answer 1

$6\cdot arcctg(3x^2+x+\sqrt3)=\pi \\\\arcctg(3x^2+x+\sqrt3)=\frac{\pi }{6}\\\\ctg\Big (arcctg(3x^2+x+\sqrt3)\Big )=ctg\frac{\pi }{6}\\\\3x^2+x+\sqrt3=\sqrt3\\\\3x^2+x=0\\\\x(3x+1)=0\\\\x_1=0\; ,\; \; x_2=- \frac{1}{3}$

Answer 2

Solving the Equation 6arccot(3x^2+x+√3)=π

To solve the equation 6arccot(3x^2+x+√3)=π, we can follow these steps:

1. Isolate the arccot term: - Start by isolating the arccot term on one side of the equation.

2. Use the arccot function: - Once the arccot term is isolated, use the properties of the arccot function to solve for the variable.

Let's proceed with these steps to solve the given equation.

Step 1: Isolate the Arccot Term

We start by isolating the arccot term on one side of the equation: 6arccot(3x^2+x+√3)=π

Step 2: Use the Arccot Function

Using the properties of the arccot function, we can rewrite the equation as: arccot(3x^2+x+√3) = π/6

Now, we have the equation in a form where we can solve for the variable inside the arccot function.

Unfortunately, the search results did not provide specific information on solving this type of equation. If you have access to a textbook or online resource that covers trigonometric equations, you may find detailed steps on how to solve equations involving the arccot function.

If you have any other questions or need further assistance, feel free to ask!