Mister Exam
arcctgx*arcctgx<=0 inequation
The solution
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acot(x)*acot(x) <= 0
$$\operatorname{acot}{\left(x \right)} \operatorname{acot}{\left(x \right)} \leq 0$$
acot(x)*acot(x) <= 0
Detail solution
Given the inequality:
$$\operatorname{acot}{\left(x \right)} \operatorname{acot}{\left(x \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{acot}{\left(x \right)} \operatorname{acot}{\left(x \right)} = 0$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$\operatorname{acot}{\left(0 \right)} \operatorname{acot}{\left(0 \right)} \leq 0$$
but
so the inequality has no solutions
$$\operatorname{acot}{\left(x \right)} \operatorname{acot}{\left(x \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{acot}{\left(x \right)} \operatorname{acot}{\left(x \right)} = 0$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$\operatorname{acot}{\left(0 \right)} \operatorname{acot}{\left(0 \right)} \leq 0$$
2
pi
--- <= 0
4
but
2
pi
--- >= 0
4
so the inequality has no solutions
Rapid solution
This inequality has no solutions