Mister Exam
tg^2×3x+tg3x>0. inequation
The solution
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2 tan (3)*x + tan(3*x) > 0
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} > 0$$
x*tan(3)^2 + tan(3*x) > 0
Detail solution
Given the inequality:
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} = 0$$
Solve:
Given the equation
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} = 0$$
transform
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} - 1 = 0$$
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} - 1 = 0$$
Do replacement
$$w = \tan{\left(3 \right)}$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = x$$
$$b = 0$$
$$c = \tan{\left(3 x \right)} - 1$$
, then
The equation has two roots.
or
$$w_{1} = \frac{\sqrt{- x \left(\tan{\left(3 x \right)} - 1\right)}}{x}$$
$$w_{2} = - \frac{\sqrt{- x \left(\tan{\left(3 x \right)} - 1\right)}}{x}$$
do backward replacement
$$\tan{\left(3 \right)} = w$$
substitute w:
$$x_{1} = -11.4430206365735$$
$$x_{2} = -13.5241732976706$$
$$x_{3} = 41.6537716005031$$
$$x_{4} = 63.5750354548075$$
$$x_{5} = 36.4394644196323$$
$$x_{6} = 61.4860527734845$$
$$x_{7} = -23.93465682743$$
$$x_{8} = -77.1582771296535$$
$$x_{9} = 69.8432464067169$$
$$x_{10} = 43.7401037273121$$
$$x_{11} = 14.5648531214347$$
$$x_{12} = -99.1137933230801$$
$$x_{13} = 83.4298541758724$$
$$x_{14} = -75.0680562341485$$
$$x_{15} = 47.9137492552259$$
$$x_{16} = -19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{18} = -4.1606760834944$$
$$x_{19} = -67.7536424860438$$
$$x_{20} = -17.6873507300709$$
$$x_{21} = 98.0680086959402$$
$$x_{22} = 28.1013912068659$$
$$x_{23} = 12.4835638214075$$
$$x_{24} = 74.0230073081604$$
$$x_{25} = 100.159601637212$$
$$x_{26} = 50.0010381242272$$
$$x_{27} = 71.9330377162168$$
$$x_{28} = -71.9330377162168$$
$$x_{29} = -91.793830738348$$
$$x_{30} = -7.28141976377463$$
$$x_{31} = 80.2939012171025$$
$$x_{32} = -6.24113746091876$$
$$x_{33} = -53.1325189107123$$
$$x_{34} = 54.1764855935747$$
$$x_{35} = 52.0886210692883$$
$$x_{36} = 19.7694282924916$$
$$x_{37} = 23.93465682743$$
$$x_{38} = 81.3391835252855$$
$$x_{39} = 37.4821465223781$$
$$x_{40} = 58.3530101922313$$
$$x_{41} = -31.2274529673745$$
$$x_{42} = -81.3391835252855$$
$$x_{43} = 10.4025393964027$$
$$x_{44} = -59.3972983233981$$
$$x_{45} = 95.9765127508869$$
$$x_{46} = -87.611596123346$$
$$x_{47} = -41.6537716005031$$
$$x_{48} = -47.9137492552259$$
$$x_{49} = -50.0010381242272$$
$$x_{50} = 15.605607050105$$
$$x_{51} = 76.1131465135857$$
$$x_{52} = -15.605607050105$$
$$x_{53} = -83.4298541758724$$
$$x_{54} = 56.2646193420575$$
$$x_{55} = 59.3972983233981$$
$$x_{56} = 26.01783227767$$
$$x_{57} = -21.8518588464878$$
$$x_{58} = -28.1013912068659$$
$$x_{59} = 34.3543772929176$$
$$x_{60} = -37.4821465223781$$
$$x_{61} = 32.2696658761755$$
$$x_{62} = -69.8432464067169$$
$$x_{63} = -95.9765127508869$$
$$x_{64} = -26.01783227767$$
$$x_{65} = -52.0886210692883$$
$$x_{66} = 2.08031316621878$$
$$x_{67} = -33.3119742070762$$
$$x_{68} = 8.32174397747159$$
$$x_{69} = 85.5206605372381$$
$$x_{70} = -35.3968743357863$$
$$x_{71} = -57.3087833759606$$
$$x_{72} = 0$$
$$x_{73} = -65.6642355039225$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{76} = -93.8851184579335$$
$$x_{77} = 17.6873507300709$$
$$x_{78} = -55.220519578813$$
$$x_{79} = 4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{81} = -45.8267669863934$$
$$x_{82} = -61.4860527734845$$
$$x_{83} = -9.36211547427728$$
$$x_{84} = 78.2034470915481$$
$$x_{85} = 87.611596123346$$
$$x_{86} = -63.5750354548075$$
$$x_{87} = -97.0222483139387$$
$$x_{88} = 39.5677822348798$$
$$x_{89} = 45.8267669863934$$
$$x_{90} = -89.7026547940409$$
$$x_{91} = -30.1853360040102$$
$$x_{92} = 6.24113746091876$$
$$x_{93} = -79.2486554340557$$
$$x_{94} = -85.5206605372381$$
$$x_{95} = 30.1853360040102$$
$$x_{96} = -74.0230073081604$$
$$x_{97} = -43.7401037273121$$
$$x_{98} = -39.5677822348798$$
$$x_{1} = -11.4430206365735$$
$$x_{2} = -13.5241732976706$$
$$x_{3} = 41.6537716005031$$
$$x_{4} = 63.5750354548075$$
$$x_{5} = 36.4394644196323$$
$$x_{6} = 61.4860527734845$$
$$x_{7} = -23.93465682743$$
$$x_{8} = -77.1582771296535$$
$$x_{9} = 69.8432464067169$$
$$x_{10} = 43.7401037273121$$
$$x_{11} = 14.5648531214347$$
$$x_{12} = -99.1137933230801$$
$$x_{13} = 83.4298541758724$$
$$x_{14} = -75.0680562341485$$
$$x_{15} = 47.9137492552259$$
$$x_{16} = -19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{18} = -4.1606760834944$$
$$x_{19} = -67.7536424860438$$
$$x_{20} = -17.6873507300709$$
$$x_{21} = 98.0680086959402$$
$$x_{22} = 28.1013912068659$$
$$x_{23} = 12.4835638214075$$
$$x_{24} = 74.0230073081604$$
$$x_{25} = 100.159601637212$$
$$x_{26} = 50.0010381242272$$
$$x_{27} = 71.9330377162168$$
$$x_{28} = -71.9330377162168$$
$$x_{29} = -91.793830738348$$
$$x_{30} = -7.28141976377463$$
$$x_{31} = 80.2939012171025$$
$$x_{32} = -6.24113746091876$$
$$x_{33} = -53.1325189107123$$
$$x_{34} = 54.1764855935747$$
$$x_{35} = 52.0886210692883$$
$$x_{36} = 19.7694282924916$$
$$x_{37} = 23.93465682743$$
$$x_{38} = 81.3391835252855$$
$$x_{39} = 37.4821465223781$$
$$x_{40} = 58.3530101922313$$
$$x_{41} = -31.2274529673745$$
$$x_{42} = -81.3391835252855$$
$$x_{43} = 10.4025393964027$$
$$x_{44} = -59.3972983233981$$
$$x_{45} = 95.9765127508869$$
$$x_{46} = -87.611596123346$$
$$x_{47} = -41.6537716005031$$
$$x_{48} = -47.9137492552259$$
$$x_{49} = -50.0010381242272$$
$$x_{50} = 15.605607050105$$
$$x_{51} = 76.1131465135857$$
$$x_{52} = -15.605607050105$$
$$x_{53} = -83.4298541758724$$
$$x_{54} = 56.2646193420575$$
$$x_{55} = 59.3972983233981$$
$$x_{56} = 26.01783227767$$
$$x_{57} = -21.8518588464878$$
$$x_{58} = -28.1013912068659$$
$$x_{59} = 34.3543772929176$$
$$x_{60} = -37.4821465223781$$
$$x_{61} = 32.2696658761755$$
$$x_{62} = -69.8432464067169$$
$$x_{63} = -95.9765127508869$$
$$x_{64} = -26.01783227767$$
$$x_{65} = -52.0886210692883$$
$$x_{66} = 2.08031316621878$$
$$x_{67} = -33.3119742070762$$
$$x_{68} = 8.32174397747159$$
$$x_{69} = 85.5206605372381$$
$$x_{70} = -35.3968743357863$$
$$x_{71} = -57.3087833759606$$
$$x_{72} = 0$$
$$x_{73} = -65.6642355039225$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{76} = -93.8851184579335$$
$$x_{77} = 17.6873507300709$$
$$x_{78} = -55.220519578813$$
$$x_{79} = 4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{81} = -45.8267669863934$$
$$x_{82} = -61.4860527734845$$
$$x_{83} = -9.36211547427728$$
$$x_{84} = 78.2034470915481$$
$$x_{85} = 87.611596123346$$
$$x_{86} = -63.5750354548075$$
$$x_{87} = -97.0222483139387$$
$$x_{88} = 39.5677822348798$$
$$x_{89} = 45.8267669863934$$
$$x_{90} = -89.7026547940409$$
$$x_{91} = -30.1853360040102$$
$$x_{92} = 6.24113746091876$$
$$x_{93} = -79.2486554340557$$
$$x_{94} = -85.5206605372381$$
$$x_{95} = 30.1853360040102$$
$$x_{96} = -74.0230073081604$$
$$x_{97} = -43.7401037273121$$
$$x_{98} = -39.5677822348798$$
This roots
$$x_{12} = -99.1137933230801$$
$$x_{87} = -97.0222483139387$$
$$x_{63} = -95.9765127508869$$
$$x_{76} = -93.8851184579335$$
$$x_{29} = -91.793830738348$$
$$x_{90} = -89.7026547940409$$
$$x_{46} = -87.611596123346$$
$$x_{94} = -85.5206605372381$$
$$x_{53} = -83.4298541758724$$
$$x_{42} = -81.3391835252855$$
$$x_{93} = -79.2486554340557$$
$$x_{8} = -77.1582771296535$$
$$x_{14} = -75.0680562341485$$
$$x_{96} = -74.0230073081604$$
$$x_{28} = -71.9330377162168$$
$$x_{62} = -69.8432464067169$$
$$x_{19} = -67.7536424860438$$
$$x_{73} = -65.6642355039225$$
$$x_{86} = -63.5750354548075$$
$$x_{82} = -61.4860527734845$$
$$x_{44} = -59.3972983233981$$
$$x_{71} = -57.3087833759606$$
$$x_{78} = -55.220519578813$$
$$x_{33} = -53.1325189107123$$
$$x_{65} = -52.0886210692883$$
$$x_{49} = -50.0010381242272$$
$$x_{48} = -47.9137492552259$$
$$x_{81} = -45.8267669863934$$
$$x_{97} = -43.7401037273121$$
$$x_{47} = -41.6537716005031$$
$$x_{98} = -39.5677822348798$$
$$x_{60} = -37.4821465223781$$
$$x_{70} = -35.3968743357863$$
$$x_{67} = -33.3119742070762$$
$$x_{41} = -31.2274529673745$$
$$x_{91} = -30.1853360040102$$
$$x_{58} = -28.1013912068659$$
$$x_{64} = -26.01783227767$$
$$x_{7} = -23.93465682743$$
$$x_{57} = -21.8518588464878$$
$$x_{16} = -19.7694282924916$$
$$x_{20} = -17.6873507300709$$
$$x_{52} = -15.605607050105$$
$$x_{2} = -13.5241732976706$$
$$x_{1} = -11.4430206365735$$
$$x_{83} = -9.36211547427728$$
$$x_{30} = -7.28141976377463$$
$$x_{32} = -6.24113746091876$$
$$x_{18} = -4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{72} = 0$$
$$x_{66} = 2.08031316621878$$
$$x_{79} = 4.1606760834944$$
$$x_{92} = 6.24113746091876$$
$$x_{68} = 8.32174397747159$$
$$x_{43} = 10.4025393964027$$
$$x_{23} = 12.4835638214075$$
$$x_{11} = 14.5648531214347$$
$$x_{50} = 15.605607050105$$
$$x_{77} = 17.6873507300709$$
$$x_{36} = 19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{37} = 23.93465682743$$
$$x_{56} = 26.01783227767$$
$$x_{22} = 28.1013912068659$$
$$x_{95} = 30.1853360040102$$
$$x_{61} = 32.2696658761755$$
$$x_{59} = 34.3543772929176$$
$$x_{5} = 36.4394644196323$$
$$x_{39} = 37.4821465223781$$
$$x_{88} = 39.5677822348798$$
$$x_{3} = 41.6537716005031$$
$$x_{10} = 43.7401037273121$$
$$x_{89} = 45.8267669863934$$
$$x_{15} = 47.9137492552259$$
$$x_{26} = 50.0010381242272$$
$$x_{35} = 52.0886210692883$$
$$x_{34} = 54.1764855935747$$
$$x_{54} = 56.2646193420575$$
$$x_{40} = 58.3530101922313$$
$$x_{55} = 59.3972983233981$$
$$x_{6} = 61.4860527734845$$
$$x_{4} = 63.5750354548075$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{9} = 69.8432464067169$$
$$x_{27} = 71.9330377162168$$
$$x_{24} = 74.0230073081604$$
$$x_{51} = 76.1131465135857$$
$$x_{84} = 78.2034470915481$$
$$x_{31} = 80.2939012171025$$
$$x_{38} = 81.3391835252855$$
$$x_{13} = 83.4298541758724$$
$$x_{69} = 85.5206605372381$$
$$x_{85} = 87.611596123346$$
$$x_{45} = 95.9765127508869$$
$$x_{21} = 98.0680086959402$$
$$x_{25} = 100.159601637212$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{12}$$
For example, let's take the point
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-99.1137933230801 + - \frac{1}{10}$$
=
$$-99.2137933230801$$
substitute to the expression
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} > 0$$
$$\left(-99.2137933230801\right) \tan^{2}{\left(3 \right)} + \tan{\left(\left(-99.2137933230801\right) 3 \right)} > 0$$
Then
$$x < -99.1137933230801$$
no execute
one of the solutions of our inequality is:
$$x > -99.1137933230801 \wedge x < -97.0222483139387$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -99.1137933230801 \wedge x < -97.0222483139387$$
$$x > -95.9765127508869 \wedge x < -93.8851184579335$$
$$x > -91.793830738348 \wedge x < -89.7026547940409$$
$$x > -87.611596123346 \wedge x < -85.5206605372381$$
$$x > -83.4298541758724 \wedge x < -81.3391835252855$$
$$x > -79.2486554340557 \wedge x < -77.1582771296535$$
$$x > -75.0680562341485 \wedge x < -74.0230073081604$$
$$x > -71.9330377162168 \wedge x < -69.8432464067169$$
$$x > -67.7536424860438 \wedge x < -65.6642355039225$$
$$x > -63.5750354548075 \wedge x < -61.4860527734845$$
$$x > -59.3972983233981 \wedge x < -57.3087833759606$$
$$x > -55.220519578813 \wedge x < -53.1325189107123$$
$$x > -52.0886210692883 \wedge x < -50.0010381242272$$
$$x > -47.9137492552259 \wedge x < -45.8267669863934$$
$$x > -43.7401037273121 \wedge x < -41.6537716005031$$
$$x > -39.5677822348798 \wedge x < -37.4821465223781$$
$$x > -35.3968743357863 \wedge x < -33.3119742070762$$
$$x > -31.2274529673745 \wedge x < -30.1853360040102$$
$$x > -28.1013912068659 \wedge x < -26.01783227767$$
$$x > -23.93465682743 \wedge x < -21.8518588464878$$
$$x > -19.7694282924916 \wedge x < -17.6873507300709$$
$$x > -15.605607050105 \wedge x < -13.5241732976706$$
$$x > -11.4430206365735 \wedge x < -9.36211547427728$$
$$x > -7.28141976377463 \wedge x < -6.24113746091876$$
$$x > -4.1606760834944 \wedge x < -2.08031316621878$$
$$x > 0 \wedge x < 2.08031316621878$$
$$x > 4.1606760834944 \wedge x < 6.24113746091876$$
$$x > 8.32174397747159 \wedge x < 10.4025393964027$$
$$x > 12.4835638214075 \wedge x < 14.5648531214347$$
$$x > 15.605607050105 \wedge x < 17.6873507300709$$
$$x > 19.7694282924916 \wedge x < 21.8518588464878$$
$$x > 23.93465682743 \wedge x < 26.01783227767$$
$$x > 28.1013912068659 \wedge x < 30.1853360040102$$
$$x > 32.2696658761755 \wedge x < 34.3543772929176$$
$$x > 36.4394644196323 \wedge x < 37.4821465223781$$
$$x > 39.5677822348798 \wedge x < 41.6537716005031$$
$$x > 43.7401037273121 \wedge x < 45.8267669863934$$
$$x > 47.9137492552259 \wedge x < 50.0010381242272$$
$$x > 52.0886210692883 \wedge x < 54.1764855935747$$
$$x > 56.2646193420575 \wedge x < 58.3530101922313$$
$$x > 59.3972983233981 \wedge x < 61.4860527734845$$
$$x > 63.5750354548075 \wedge x < 65.6642355039225$$
$$x > 67.7536424860438 \wedge x < 69.8432464067169$$
$$x > 71.9330377162168 \wedge x < 74.0230073081604$$
$$x > 76.1131465135857 \wedge x < 78.2034470915481$$
$$x > 80.2939012171025 \wedge x < 81.3391835252855$$
$$x > 83.4298541758724 \wedge x < 85.5206605372381$$
$$x > 87.611596123346 \wedge x < 95.9765127508869$$
$$x > 98.0680086959402 \wedge x < 100.159601637212$$
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} = 0$$
Solve:
Given the equation
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} = 0$$
transform
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} - 1 = 0$$
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} - 1 = 0$$
Do replacement
$$w = \tan{\left(3 \right)}$$
This equation is of the form
a*w^2 + b*w + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = x$$
$$b = 0$$
$$c = \tan{\left(3 x \right)} - 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (x) * (-1 + tan(3*x)) = -4*x*(-1 + tan(3*x))
The equation has two roots.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
or
$$w_{1} = \frac{\sqrt{- x \left(\tan{\left(3 x \right)} - 1\right)}}{x}$$
$$w_{2} = - \frac{\sqrt{- x \left(\tan{\left(3 x \right)} - 1\right)}}{x}$$
do backward replacement
$$\tan{\left(3 \right)} = w$$
substitute w:
$$x_{1} = -11.4430206365735$$
$$x_{2} = -13.5241732976706$$
$$x_{3} = 41.6537716005031$$
$$x_{4} = 63.5750354548075$$
$$x_{5} = 36.4394644196323$$
$$x_{6} = 61.4860527734845$$
$$x_{7} = -23.93465682743$$
$$x_{8} = -77.1582771296535$$
$$x_{9} = 69.8432464067169$$
$$x_{10} = 43.7401037273121$$
$$x_{11} = 14.5648531214347$$
$$x_{12} = -99.1137933230801$$
$$x_{13} = 83.4298541758724$$
$$x_{14} = -75.0680562341485$$
$$x_{15} = 47.9137492552259$$
$$x_{16} = -19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{18} = -4.1606760834944$$
$$x_{19} = -67.7536424860438$$
$$x_{20} = -17.6873507300709$$
$$x_{21} = 98.0680086959402$$
$$x_{22} = 28.1013912068659$$
$$x_{23} = 12.4835638214075$$
$$x_{24} = 74.0230073081604$$
$$x_{25} = 100.159601637212$$
$$x_{26} = 50.0010381242272$$
$$x_{27} = 71.9330377162168$$
$$x_{28} = -71.9330377162168$$
$$x_{29} = -91.793830738348$$
$$x_{30} = -7.28141976377463$$
$$x_{31} = 80.2939012171025$$
$$x_{32} = -6.24113746091876$$
$$x_{33} = -53.1325189107123$$
$$x_{34} = 54.1764855935747$$
$$x_{35} = 52.0886210692883$$
$$x_{36} = 19.7694282924916$$
$$x_{37} = 23.93465682743$$
$$x_{38} = 81.3391835252855$$
$$x_{39} = 37.4821465223781$$
$$x_{40} = 58.3530101922313$$
$$x_{41} = -31.2274529673745$$
$$x_{42} = -81.3391835252855$$
$$x_{43} = 10.4025393964027$$
$$x_{44} = -59.3972983233981$$
$$x_{45} = 95.9765127508869$$
$$x_{46} = -87.611596123346$$
$$x_{47} = -41.6537716005031$$
$$x_{48} = -47.9137492552259$$
$$x_{49} = -50.0010381242272$$
$$x_{50} = 15.605607050105$$
$$x_{51} = 76.1131465135857$$
$$x_{52} = -15.605607050105$$
$$x_{53} = -83.4298541758724$$
$$x_{54} = 56.2646193420575$$
$$x_{55} = 59.3972983233981$$
$$x_{56} = 26.01783227767$$
$$x_{57} = -21.8518588464878$$
$$x_{58} = -28.1013912068659$$
$$x_{59} = 34.3543772929176$$
$$x_{60} = -37.4821465223781$$
$$x_{61} = 32.2696658761755$$
$$x_{62} = -69.8432464067169$$
$$x_{63} = -95.9765127508869$$
$$x_{64} = -26.01783227767$$
$$x_{65} = -52.0886210692883$$
$$x_{66} = 2.08031316621878$$
$$x_{67} = -33.3119742070762$$
$$x_{68} = 8.32174397747159$$
$$x_{69} = 85.5206605372381$$
$$x_{70} = -35.3968743357863$$
$$x_{71} = -57.3087833759606$$
$$x_{72} = 0$$
$$x_{73} = -65.6642355039225$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{76} = -93.8851184579335$$
$$x_{77} = 17.6873507300709$$
$$x_{78} = -55.220519578813$$
$$x_{79} = 4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{81} = -45.8267669863934$$
$$x_{82} = -61.4860527734845$$
$$x_{83} = -9.36211547427728$$
$$x_{84} = 78.2034470915481$$
$$x_{85} = 87.611596123346$$
$$x_{86} = -63.5750354548075$$
$$x_{87} = -97.0222483139387$$
$$x_{88} = 39.5677822348798$$
$$x_{89} = 45.8267669863934$$
$$x_{90} = -89.7026547940409$$
$$x_{91} = -30.1853360040102$$
$$x_{92} = 6.24113746091876$$
$$x_{93} = -79.2486554340557$$
$$x_{94} = -85.5206605372381$$
$$x_{95} = 30.1853360040102$$
$$x_{96} = -74.0230073081604$$
$$x_{97} = -43.7401037273121$$
$$x_{98} = -39.5677822348798$$
$$x_{1} = -11.4430206365735$$
$$x_{2} = -13.5241732976706$$
$$x_{3} = 41.6537716005031$$
$$x_{4} = 63.5750354548075$$
$$x_{5} = 36.4394644196323$$
$$x_{6} = 61.4860527734845$$
$$x_{7} = -23.93465682743$$
$$x_{8} = -77.1582771296535$$
$$x_{9} = 69.8432464067169$$
$$x_{10} = 43.7401037273121$$
$$x_{11} = 14.5648531214347$$
$$x_{12} = -99.1137933230801$$
$$x_{13} = 83.4298541758724$$
$$x_{14} = -75.0680562341485$$
$$x_{15} = 47.9137492552259$$
$$x_{16} = -19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{18} = -4.1606760834944$$
$$x_{19} = -67.7536424860438$$
$$x_{20} = -17.6873507300709$$
$$x_{21} = 98.0680086959402$$
$$x_{22} = 28.1013912068659$$
$$x_{23} = 12.4835638214075$$
$$x_{24} = 74.0230073081604$$
$$x_{25} = 100.159601637212$$
$$x_{26} = 50.0010381242272$$
$$x_{27} = 71.9330377162168$$
$$x_{28} = -71.9330377162168$$
$$x_{29} = -91.793830738348$$
$$x_{30} = -7.28141976377463$$
$$x_{31} = 80.2939012171025$$
$$x_{32} = -6.24113746091876$$
$$x_{33} = -53.1325189107123$$
$$x_{34} = 54.1764855935747$$
$$x_{35} = 52.0886210692883$$
$$x_{36} = 19.7694282924916$$
$$x_{37} = 23.93465682743$$
$$x_{38} = 81.3391835252855$$
$$x_{39} = 37.4821465223781$$
$$x_{40} = 58.3530101922313$$
$$x_{41} = -31.2274529673745$$
$$x_{42} = -81.3391835252855$$
$$x_{43} = 10.4025393964027$$
$$x_{44} = -59.3972983233981$$
$$x_{45} = 95.9765127508869$$
$$x_{46} = -87.611596123346$$
$$x_{47} = -41.6537716005031$$
$$x_{48} = -47.9137492552259$$
$$x_{49} = -50.0010381242272$$
$$x_{50} = 15.605607050105$$
$$x_{51} = 76.1131465135857$$
$$x_{52} = -15.605607050105$$
$$x_{53} = -83.4298541758724$$
$$x_{54} = 56.2646193420575$$
$$x_{55} = 59.3972983233981$$
$$x_{56} = 26.01783227767$$
$$x_{57} = -21.8518588464878$$
$$x_{58} = -28.1013912068659$$
$$x_{59} = 34.3543772929176$$
$$x_{60} = -37.4821465223781$$
$$x_{61} = 32.2696658761755$$
$$x_{62} = -69.8432464067169$$
$$x_{63} = -95.9765127508869$$
$$x_{64} = -26.01783227767$$
$$x_{65} = -52.0886210692883$$
$$x_{66} = 2.08031316621878$$
$$x_{67} = -33.3119742070762$$
$$x_{68} = 8.32174397747159$$
$$x_{69} = 85.5206605372381$$
$$x_{70} = -35.3968743357863$$
$$x_{71} = -57.3087833759606$$
$$x_{72} = 0$$
$$x_{73} = -65.6642355039225$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{76} = -93.8851184579335$$
$$x_{77} = 17.6873507300709$$
$$x_{78} = -55.220519578813$$
$$x_{79} = 4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{81} = -45.8267669863934$$
$$x_{82} = -61.4860527734845$$
$$x_{83} = -9.36211547427728$$
$$x_{84} = 78.2034470915481$$
$$x_{85} = 87.611596123346$$
$$x_{86} = -63.5750354548075$$
$$x_{87} = -97.0222483139387$$
$$x_{88} = 39.5677822348798$$
$$x_{89} = 45.8267669863934$$
$$x_{90} = -89.7026547940409$$
$$x_{91} = -30.1853360040102$$
$$x_{92} = 6.24113746091876$$
$$x_{93} = -79.2486554340557$$
$$x_{94} = -85.5206605372381$$
$$x_{95} = 30.1853360040102$$
$$x_{96} = -74.0230073081604$$
$$x_{97} = -43.7401037273121$$
$$x_{98} = -39.5677822348798$$
This roots
$$x_{12} = -99.1137933230801$$
$$x_{87} = -97.0222483139387$$
$$x_{63} = -95.9765127508869$$
$$x_{76} = -93.8851184579335$$
$$x_{29} = -91.793830738348$$
$$x_{90} = -89.7026547940409$$
$$x_{46} = -87.611596123346$$
$$x_{94} = -85.5206605372381$$
$$x_{53} = -83.4298541758724$$
$$x_{42} = -81.3391835252855$$
$$x_{93} = -79.2486554340557$$
$$x_{8} = -77.1582771296535$$
$$x_{14} = -75.0680562341485$$
$$x_{96} = -74.0230073081604$$
$$x_{28} = -71.9330377162168$$
$$x_{62} = -69.8432464067169$$
$$x_{19} = -67.7536424860438$$
$$x_{73} = -65.6642355039225$$
$$x_{86} = -63.5750354548075$$
$$x_{82} = -61.4860527734845$$
$$x_{44} = -59.3972983233981$$
$$x_{71} = -57.3087833759606$$
$$x_{78} = -55.220519578813$$
$$x_{33} = -53.1325189107123$$
$$x_{65} = -52.0886210692883$$
$$x_{49} = -50.0010381242272$$
$$x_{48} = -47.9137492552259$$
$$x_{81} = -45.8267669863934$$
$$x_{97} = -43.7401037273121$$
$$x_{47} = -41.6537716005031$$
$$x_{98} = -39.5677822348798$$
$$x_{60} = -37.4821465223781$$
$$x_{70} = -35.3968743357863$$
$$x_{67} = -33.3119742070762$$
$$x_{41} = -31.2274529673745$$
$$x_{91} = -30.1853360040102$$
$$x_{58} = -28.1013912068659$$
$$x_{64} = -26.01783227767$$
$$x_{7} = -23.93465682743$$
$$x_{57} = -21.8518588464878$$
$$x_{16} = -19.7694282924916$$
$$x_{20} = -17.6873507300709$$
$$x_{52} = -15.605607050105$$
$$x_{2} = -13.5241732976706$$
$$x_{1} = -11.4430206365735$$
$$x_{83} = -9.36211547427728$$
$$x_{30} = -7.28141976377463$$
$$x_{32} = -6.24113746091876$$
$$x_{18} = -4.1606760834944$$
$$x_{80} = -2.08031316621878$$
$$x_{72} = 0$$
$$x_{66} = 2.08031316621878$$
$$x_{79} = 4.1606760834944$$
$$x_{92} = 6.24113746091876$$
$$x_{68} = 8.32174397747159$$
$$x_{43} = 10.4025393964027$$
$$x_{23} = 12.4835638214075$$
$$x_{11} = 14.5648531214347$$
$$x_{50} = 15.605607050105$$
$$x_{77} = 17.6873507300709$$
$$x_{36} = 19.7694282924916$$
$$x_{17} = 21.8518588464878$$
$$x_{37} = 23.93465682743$$
$$x_{56} = 26.01783227767$$
$$x_{22} = 28.1013912068659$$
$$x_{95} = 30.1853360040102$$
$$x_{61} = 32.2696658761755$$
$$x_{59} = 34.3543772929176$$
$$x_{5} = 36.4394644196323$$
$$x_{39} = 37.4821465223781$$
$$x_{88} = 39.5677822348798$$
$$x_{3} = 41.6537716005031$$
$$x_{10} = 43.7401037273121$$
$$x_{89} = 45.8267669863934$$
$$x_{15} = 47.9137492552259$$
$$x_{26} = 50.0010381242272$$
$$x_{35} = 52.0886210692883$$
$$x_{34} = 54.1764855935747$$
$$x_{54} = 56.2646193420575$$
$$x_{40} = 58.3530101922313$$
$$x_{55} = 59.3972983233981$$
$$x_{6} = 61.4860527734845$$
$$x_{4} = 63.5750354548075$$
$$x_{74} = 65.6642355039225$$
$$x_{75} = 67.7536424860438$$
$$x_{9} = 69.8432464067169$$
$$x_{27} = 71.9330377162168$$
$$x_{24} = 74.0230073081604$$
$$x_{51} = 76.1131465135857$$
$$x_{84} = 78.2034470915481$$
$$x_{31} = 80.2939012171025$$
$$x_{38} = 81.3391835252855$$
$$x_{13} = 83.4298541758724$$
$$x_{69} = 85.5206605372381$$
$$x_{85} = 87.611596123346$$
$$x_{45} = 95.9765127508869$$
$$x_{21} = 98.0680086959402$$
$$x_{25} = 100.159601637212$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{12}$$
For example, let's take the point
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-99.1137933230801 + - \frac{1}{10}$$
=
$$-99.2137933230801$$
substitute to the expression
$$x \tan^{2}{\left(3 \right)} + \tan{\left(3 x \right)} > 0$$
$$\left(-99.2137933230801\right) \tan^{2}{\left(3 \right)} + \tan{\left(\left(-99.2137933230801\right) 3 \right)} > 0$$
2
1.05029134212031 - 99.2137933230801*tan (3) > 0
Then
$$x < -99.1137933230801$$
no execute
one of the solutions of our inequality is:
$$x > -99.1137933230801 \wedge x < -97.0222483139387$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x12 x87 x63 x76 x29 x90 x46 x94 x53 x42 x93 x8 x14 x96 x28 x62 x19 x73 x86 x82 x44 x71 x78 x33 x65 x49 x48 x81 x97 x47 x98 x60 x70 x67 x41 x91 x58 x64 x7 x57 x16 x20 x52 x2 x1 x83 x30 x32 x18 x80 x72 x66 x79 x92 x68 x43 x23 x11 x50 x77 x36 x17 x37 x56 x22 x95 x61 x59 x5 x39 x88 x3 x10 x89 x15 x26 x35 x34 x54 x40 x55 x6 x4 x74 x75 x9 x27 x24 x51 x84 x31 x38 x13 x69 x85 x45 x21 x25Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -99.1137933230801 \wedge x < -97.0222483139387$$
$$x > -95.9765127508869 \wedge x < -93.8851184579335$$
$$x > -91.793830738348 \wedge x < -89.7026547940409$$
$$x > -87.611596123346 \wedge x < -85.5206605372381$$
$$x > -83.4298541758724 \wedge x < -81.3391835252855$$
$$x > -79.2486554340557 \wedge x < -77.1582771296535$$
$$x > -75.0680562341485 \wedge x < -74.0230073081604$$
$$x > -71.9330377162168 \wedge x < -69.8432464067169$$
$$x > -67.7536424860438 \wedge x < -65.6642355039225$$
$$x > -63.5750354548075 \wedge x < -61.4860527734845$$
$$x > -59.3972983233981 \wedge x < -57.3087833759606$$
$$x > -55.220519578813 \wedge x < -53.1325189107123$$
$$x > -52.0886210692883 \wedge x < -50.0010381242272$$
$$x > -47.9137492552259 \wedge x < -45.8267669863934$$
$$x > -43.7401037273121 \wedge x < -41.6537716005031$$
$$x > -39.5677822348798 \wedge x < -37.4821465223781$$
$$x > -35.3968743357863 \wedge x < -33.3119742070762$$
$$x > -31.2274529673745 \wedge x < -30.1853360040102$$
$$x > -28.1013912068659 \wedge x < -26.01783227767$$
$$x > -23.93465682743 \wedge x < -21.8518588464878$$
$$x > -19.7694282924916 \wedge x < -17.6873507300709$$
$$x > -15.605607050105 \wedge x < -13.5241732976706$$
$$x > -11.4430206365735 \wedge x < -9.36211547427728$$
$$x > -7.28141976377463 \wedge x < -6.24113746091876$$
$$x > -4.1606760834944 \wedge x < -2.08031316621878$$
$$x > 0 \wedge x < 2.08031316621878$$
$$x > 4.1606760834944 \wedge x < 6.24113746091876$$
$$x > 8.32174397747159 \wedge x < 10.4025393964027$$
$$x > 12.4835638214075 \wedge x < 14.5648531214347$$
$$x > 15.605607050105 \wedge x < 17.6873507300709$$
$$x > 19.7694282924916 \wedge x < 21.8518588464878$$
$$x > 23.93465682743 \wedge x < 26.01783227767$$
$$x > 28.1013912068659 \wedge x < 30.1853360040102$$
$$x > 32.2696658761755 \wedge x < 34.3543772929176$$
$$x > 36.4394644196323 \wedge x < 37.4821465223781$$
$$x > 39.5677822348798 \wedge x < 41.6537716005031$$
$$x > 43.7401037273121 \wedge x < 45.8267669863934$$
$$x > 47.9137492552259 \wedge x < 50.0010381242272$$
$$x > 52.0886210692883 \wedge x < 54.1764855935747$$
$$x > 56.2646193420575 \wedge x < 58.3530101922313$$
$$x > 59.3972983233981 \wedge x < 61.4860527734845$$
$$x > 63.5750354548075 \wedge x < 65.6642355039225$$
$$x > 67.7536424860438 \wedge x < 69.8432464067169$$
$$x > 71.9330377162168 \wedge x < 74.0230073081604$$
$$x > 76.1131465135857 \wedge x < 78.2034470915481$$
$$x > 80.2939012171025 \wedge x < 81.3391835252855$$
$$x > 83.4298541758724 \wedge x < 85.5206605372381$$
$$x > 87.611596123346 \wedge x < 95.9765127508869$$
$$x > 98.0680086959402 \wedge x < 100.159601637212$$
Solving inequality on a graph