Mister Exam
10/(100-x^2)<0 inequation
The solution
Detail solution
Given the inequality:
$$\frac{10}{100 - x^{2}} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{10}{100 - x^{2}} = 0$$
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
$$\frac{10}{100 - 0^{2}} < 0$$
but
so the inequality has no solutions
$$\frac{10}{100 - x^{2}} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{10}{100 - x^{2}} = 0$$
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
$$\frac{10}{100 - 0^{2}} < 0$$
1/10 < 0
but
1/10 > 0
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
[src]
Or(And(-oo < x, x < -10), And(10 < x, x < oo))
$$\left(-\infty < x \wedge x < -10\right) \vee \left(10 < x \wedge x < \infty\right)$$
((-oo < x)∧(x < -10))∨((10 < x)∧(x < oo))
Rapid solution 2
[src]
(-oo, -10) U (10, oo)
$$x\ in\ \left(-\infty, -10\right) \cup \left(10, \infty\right)$$
x in Union(Interval.open(-oo, -10), Interval.open(10, oo))