Mister Exam
-16/((x+2)²-5)≥0 inequation
The solution
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[src]
-16
------------ >= 0
2
(x + 2) - 5
$$- \frac{16}{\left(x + 2\right)^{2} - 5} \geq 0$$
-16/((x + 2)^2 - 5) >= 0
Detail solution
Given the inequality:
$$- \frac{16}{\left(x + 2\right)^{2} - 5} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{16}{\left(x + 2\right)^{2} - 5} = 0$$
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
$$- \frac{16}{-5 + 2^{2}} \geq 0$$
so the inequality is always executed
$$- \frac{16}{\left(x + 2\right)^{2} - 5} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{16}{\left(x + 2\right)^{2} - 5} = 0$$
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
$$- \frac{16}{-5 + 2^{2}} \geq 0$$
16 >= 0
so the inequality is always executed
Solving inequality on a graph
Rapid solution 2
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___ ___ (-2 - \/ 5 , -2 + \/ 5 )
$$x\ in\ \left(- \sqrt{5} - 2, -2 + \sqrt{5}\right)$$
x in Interval.open(-sqrt(5) - 2, -2 + sqrt(5))
Rapid solution
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/ ___ ___ \ And\x < -2 + \/ 5 , -2 - \/ 5 < x/
$$x < -2 + \sqrt{5} \wedge - \sqrt{5} - 2 < x$$
(x < -2 + sqrt(5))∧(-2 - sqrt(5) < x)