Mister Exam
-5/(x-2)^2<0 inequation
The solution
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-5
-------- < 0
2
(x - 2)
$$- \frac{5}{\left(x - 2\right)^{2}} < 0$$
-5/(x - 2)^2 < 0
Detail solution
Given the inequality:
$$- \frac{5}{\left(x - 2\right)^{2}} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{5}{\left(x - 2\right)^{2}} = 0$$
Solve:
Given the equation
$$- \frac{5}{\left(x - 2\right)^{2}} = 0$$
Because equation degree is equal to = -2 < 0 and the free term = 0
so the solutions of the equation d'not exist
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
$$- \frac{5}{\left(-2\right)^{2}} < 0$$
so the inequality is always executed
$$- \frac{5}{\left(x - 2\right)^{2}} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{5}{\left(x - 2\right)^{2}} = 0$$
Solve:
Given the equation
$$- \frac{5}{\left(x - 2\right)^{2}} = 0$$
Because equation degree is equal to = -2 < 0 and the free term = 0
so the solutions of the equation d'not exist
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
$$- \frac{5}{\left(-2\right)^{2}} < 0$$
-5/4 < 0
so the inequality is always executed
Solving inequality on a graph
Rapid solution
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And(x > -oo, x < oo, x != 2)
$$x > -\infty \wedge x < \infty \wedge x \neq 2$$
(x > -oo)∧(x < oo)∧(Ne(x, 2))
Rapid solution 2
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(-oo, 2) U (2, oo)
$$x\ in\ \left(-\infty, 2\right) \cup \left(2, \infty\right)$$
x in Union(Interval.open(-oo, 2), Interval.open(2, oo))