Mister Exam
arctg^2(x)-4arctgx+3>0 inequation
The solution
You have entered
[src]
2 atan (x) - 4*acot(x) + 3 > 0
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 > 0$$
-4*acot(x) + atan(x)^2 + 3 > 0
Detail solution
Given the inequality:
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 = 0$$
Solve:
$$x_{1} = 0.840132875044046$$
$$x_{1} = 0.840132875044046$$
This roots
$$x_{1} = 0.840132875044046$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0.840132875044046$$
=
$$0.740132875044046$$
substitute to the expression
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 > 0$$
$$\left(- 4 \operatorname{acot}{\left(0.740132875044046 \right)} + \operatorname{atan}^{2}{\left(0.740132875044046 \right)}\right) + 3 > 0$$
Then
$$x < 0.840132875044046$$
no execute
the solution of our inequality is:
$$x > 0.840132875044046$$
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 = 0$$
Solve:
$$x_{1} = 0.840132875044046$$
$$x_{1} = 0.840132875044046$$
This roots
$$x_{1} = 0.840132875044046$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0.840132875044046$$
=
$$0.740132875044046$$
substitute to the expression
$$\left(- 4 \operatorname{acot}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)}\right) + 3 > 0$$
$$\left(- 4 \operatorname{acot}{\left(0.740132875044046 \right)} + \operatorname{atan}^{2}{\left(0.740132875044046 \right)}\right) + 3 > 0$$
-0.328592575763513 > 0
Then
$$x < 0.840132875044046$$
no execute
the solution of our inequality is:
$$x > 0.840132875044046$$
_____
/
-------ο-------
x1