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# Solving quadratic inequality

How to solve the following quadratic inequality:

$$0.3 < \frac{2x}{x^{2} + 4} <0.5$$

The call to solve function return the following output:

sage:
sage: solve( [(2*x / (4+x**2)) < .5 , (2*x / (x**2 + 4)) > .3 ], x, to_poly_serve=True )
[[-2*x/(x^2 + 4) + 0.5 > 0, 2*x/(x^2 + 4) - 0.3 > 0]]
sage:


By hand calculation I found the following answer $(2/3, 2) \cup (2, 6)$.

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## 1 Answer

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Symbolic and numerical do not like eachother, instead of 0.5 and 0.3, use 1/2 and 3/10 :

sage: solve( [(2*x / (4+x**2)) < 1/2 , (2*x / (x**2 + 4)) > 3/10 ], x)
[[(2/3) < x, x < 6, x - 2 != 0]]

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## Comments

but the answer doesn't contain the last part (2, 6)

( 2020-05-08 19:40:27 +0200 )edit
2

Yes, it does: the first two inequalities define the interval $(2/3,6)$, the last term removes ${2}$ from the interval.

( 2020-05-08 19:42:48 +0200 )edit

Thanks, I didn't notice it.

( 2020-05-09 06:50:16 +0200 )edit

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Asked: 2020-05-08 19:31:51 +0200

Seen: 89 times

Last updated: May 09 '20