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Expresiones idénticas
- dos (tg(x))^ cuatro + dieciséis *sqrt(tres)(tg(x))^ tres - trece (tg(x))^ dos - siete = cero
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- 2(tg(x))^4+16*√(3)(tg(x))^3-13(tg(x))^2-7=0
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Expresiones semejantes
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Expresiones con funciones
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2(tg(x))^4+16*sqrt(3)(tg(x))^3-13(tg(x))^2-7=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 ___ 3 2 2*tan (x) + 16*\/ 3 *tan (x) - 13*tan (x) - 7 = 0
$$\left(\left(2 \tan^{4}{\left(x \right)} + 16 \sqrt{3} \tan^{3}{\left(x \right)}\right) - 13 \tan^{2}{\left(x \right)}\right) - 7 = 0$$
Respuesta rápida
[src]
/ / _________________________________________________________________________________________________________________________________________________________________ \\ / / _________________________________________________________________________________________________________________________________________________________________ \\
| | / ________________________ || | | / ________________________ ||
| | / / __________ ___ || | | / / __________ ___ ||
| | / 314 / 81325 \/ 20412826 1 436*\/ 3 || | | / 314 / 81325 \/ 20412826 1 436*\/ 3 ||
| | / --- - 2*3 / - ----- + ------------ - -------------------------------- - ------------------------------------------------------------------------------------ || | | / --- - 2*3 / - ----- + ------------ - -------------------------------- - ------------------------------------------------------------------------------------ ||
| | __________________________________________________________________________ / 3 \/ 1728 96 ________________________ __________________________________________________________________________ || | | __________________________________________________________________________ / 3 \/ 1728 96 ________________________ __________________________________________________________________________ ||
| | / ________________________ / / __________ / ________________________ || | | / ________________________ / / __________ / ________________________ ||
| | / / __________ / / 81325 \/ 20412826 / / __________ || | | / / __________ / / 81325 \/ 20412826 / / __________ ||
| | / 157 / 81325 \/ 20412826 1 / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 || | | / 157 / 81325 \/ 20412826 1 / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 ||
| | / --- + 2*3 / - ----- + ------------ + -------------------------------- / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- || | | / --- + 2*3 / - ----- + ------------ + -------------------------------- / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- ||
| | / 3 \/ 1728 96 ________________________ / / 3 \/ 1728 96 ________________________ || | | / 3 \/ 1728 96 ________________________ / / 3 \/ 1728 96 ________________________ ||
| | / / __________ / / / __________ || | | / / __________ / / / __________ ||
| | / / 81325 \/ 20412826 / / / 81325 \/ 20412826 || | | / / 81325 \/ 20412826 / / / 81325 \/ 20412826 ||
| | / 72*3 / - ----- + ------------ / / 72*3 / - ----- + ------------ || | | / 72*3 / - ----- + ------------ / / 72*3 / - ----- + ------------ ||
| |\/ \/ 1728 96 \/ \/ \/ 1728 96 ___|| | |\/ \/ 1728 96 \/ \/ \/ 1728 96 ___||
x1 = I*im|atan|------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 2*\/ 3 || + re|atan|------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 2*\/ 3 ||
\ \ 2 2 // \ \ 2 2 //
$$x_{1} = \operatorname{re}{\left(\operatorname{atan}{\left(- 2 \sqrt{3} + \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} + \frac{\sqrt{\frac{314}{3} - \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- 2 \sqrt{3} + \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} + \frac{\sqrt{\frac{314}{3} - \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} \right)}\right)}$$
/ / _________________________________________________________________________________________________________________________________________________________________ \\ / / _________________________________________________________________________________________________________________________________________________________________ \\
| | / ________________________ || | | / ________________________ ||
| | / / __________ ___ || | | / / __________ ___ ||
| | / 314 / 81325 \/ 20412826 1 436*\/ 3 || | | / 314 / 81325 \/ 20412826 1 436*\/ 3 ||
| | / --- - 2*3 / - ----- + ------------ - -------------------------------- - ------------------------------------------------------------------------------------ || | | / --- - 2*3 / - ----- + ------------ - -------------------------------- - ------------------------------------------------------------------------------------ ||
| | / 3 \/ 1728 96 ________________________ __________________________________________________________________________ __________________________________________________________________________|| | | / 3 \/ 1728 96 ________________________ __________________________________________________________________________ __________________________________________________________________________||
| | / / __________ / ________________________ / ________________________ || | | / / __________ / ________________________ / ________________________ ||
| | / / 81325 \/ 20412826 / / __________ / / __________ || | | / / 81325 \/ 20412826 / / __________ / / __________ ||
| | / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 / 157 / 81325 \/ 20412826 1 || | | / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 / 157 / 81325 \/ 20412826 1 ||
| | / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- / --- + 2*3 / - ----- + ------------ + -------------------------------- || | | / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- / --- + 2*3 / - ----- + ------------ + -------------------------------- ||
| | / / 3 \/ 1728 96 ________________________ / 3 \/ 1728 96 ________________________ || | | / / 3 \/ 1728 96 ________________________ / 3 \/ 1728 96 ________________________ ||
| | / / / __________ / / __________ || | | / / / __________ / / __________ ||
| | / / / 81325 \/ 20412826 / / 81325 \/ 20412826 || | | / / / 81325 \/ 20412826 / / 81325 \/ 20412826 ||
| | / / 72*3 / - ----- + ------------ / 72*3 / - ----- + ------------ || | | / / 72*3 / - ----- + ------------ / 72*3 / - ----- + ------------ ||
| |\/ \/ \/ 1728 96 ___ \/ \/ 1728 96 || | |\/ \/ \/ 1728 96 ___ \/ \/ 1728 96 ||
x2 = - re|atan|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*\/ 3 - ------------------------------------------------------------------------------------|| - I*im|atan|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*\/ 3 - ------------------------------------------------------------------------------------||
\ \ 2 2 // \ \ 2 2 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{atan}{\left(2 \sqrt{3} - \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} + \frac{\sqrt{\frac{314}{3} - \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(2 \sqrt{3} - \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} + \frac{\sqrt{\frac{314}{3} - \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} \right)}\right)}$$
/ _________________________________________________________________________________________________________________________________________________________________ \
| / ________________________ |
| / / __________ ___ |
| / 314 / 81325 \/ 20412826 1 436*\/ 3 |
| / --- - 2*3 / - ----- + ------------ - -------------------------------- + ------------------------------------------------------------------------------------ |
| __________________________________________________________________________ / 3 \/ 1728 96 ________________________ __________________________________________________________________________ |
| / ________________________ / / __________ / ________________________ |
| / / __________ / / 81325 \/ 20412826 / / __________ |
| / 157 / 81325 \/ 20412826 1 / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 |
| / --- + 2*3 / - ----- + ------------ + -------------------------------- / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- |
| / 3 \/ 1728 96 ________________________ / / 3 \/ 1728 96 ________________________ |
| / / __________ / / / __________ |
| / / 81325 \/ 20412826 / / / 81325 \/ 20412826 |
| / 72*3 / - ----- + ------------ / / 72*3 / - ----- + ------------ |
|\/ \/ 1728 96 \/ \/ \/ 1728 96 ___|
x3 = -atan|------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*\/ 3 |
\ 2 2 /
$$x_{3} = - \operatorname{atan}{\left(2 \sqrt{3} + \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} + \frac{\sqrt{\frac{314}{3} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} + \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} \right)}$$
/ / _________________________________________________________________________________________________________________________________________________________________\\ / / _________________________________________________________________________________________________________________________________________________________________\\
| | / ________________________ || | | / ________________________ ||
| | / / __________ ___ || | | / / __________ ___ ||
| | / 314 / 81325 \/ 20412826 1 436*\/ 3 || | | / 314 / 81325 \/ 20412826 1 436*\/ 3 ||
| | / --- - 2*3 / - ----- + ------------ - -------------------------------- + ------------------------------------------------------------------------------------ || | | / --- - 2*3 / - ----- + ------------ - -------------------------------- + ------------------------------------------------------------------------------------ ||
| | __________________________________________________________________________ / 3 \/ 1728 96 ________________________ __________________________________________________________________________ || | | __________________________________________________________________________ / 3 \/ 1728 96 ________________________ __________________________________________________________________________ ||
| | / ________________________ / / __________ / ________________________ || | | / ________________________ / / __________ / ________________________ ||
| | / / __________ / / 81325 \/ 20412826 / / __________ || | | / / __________ / / 81325 \/ 20412826 / / __________ ||
| | / 157 / 81325 \/ 20412826 1 / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 || | | / 157 / 81325 \/ 20412826 1 / 72*3 / - ----- + ------------ / 157 / 81325 \/ 20412826 1 ||
| | / --- + 2*3 / - ----- + ------------ + -------------------------------- / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- || | | / --- + 2*3 / - ----- + ------------ + -------------------------------- / \/ 1728 96 / --- + 2*3 / - ----- + ------------ + -------------------------------- ||
| | / 3 \/ 1728 96 ________________________ / / 3 \/ 1728 96 ________________________ || | | / 3 \/ 1728 96 ________________________ / / 3 \/ 1728 96 ________________________ ||
| | / / __________ / / / __________ || | | / / __________ / / / __________ ||
| | / / 81325 \/ 20412826 / / / 81325 \/ 20412826 || | | / / 81325 \/ 20412826 / / / 81325 \/ 20412826 ||
| | / 72*3 / - ----- + ------------ / / 72*3 / - ----- + ------------ || | | / 72*3 / - ----- + ------------ / / 72*3 / - ----- + ------------ ||
| |\/ \/ 1728 96 ___ \/ \/ \/ 1728 96 || | |\/ \/ 1728 96 ___ \/ \/ \/ 1728 96 ||
x4 = - re|atan|------------------------------------------------------------------------------------ + 2*\/ 3 - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| - I*im|atan|------------------------------------------------------------------------------------ + 2*\/ 3 - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
\ \ 2 2 // \ \ 2 2 //
$$x_{4} = - \operatorname{re}{\left(\operatorname{atan}{\left(2 \sqrt{3} - \frac{\sqrt{\frac{314}{3} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} + \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} + \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(2 \sqrt{3} - \frac{\sqrt{\frac{314}{3} - 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}} + \frac{436 \sqrt{3}}{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}} - \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}}{2} + \frac{\sqrt{\frac{157}{3} + \frac{1}{72 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}} + 2 \sqrt[3]{- \frac{81325}{1728} + \frac{\sqrt{20412826}}{96}}}}{2} \right)}\right)}$$
x4 = -re(atan(2*sqrt(3) - sqrt(314/3 - 2*(-81325/1728 + sqrt(20412826)/96)^(1/3) + 436*sqrt(3)/sqrt(157/3 + 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)) + 2*(-81325/1728 + sqrt(20412826)/96)^(1/3)) - 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)))/2 + sqrt(157/3 + 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)) + 2*(-81325/1728 + sqrt(20412826)/96)^(1/3))/2)) - i*im(atan(2*sqrt(3) - sqrt(314/3 - 2*(-81325/1728 + sqrt(20412826)/96)^(1/3) + 436*sqrt(3)/sqrt(157/3 + 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)) + 2*(-81325/1728 + sqrt(20412826)/96)^(1/3)) - 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)))/2 + sqrt(157/3 + 1/(72*(-81325/1728 + sqrt(20412826)/96)^(1/3)) + 2*(-81325/1728 + sqrt(20412826)/96)^(1/3))/2))
Respuesta numérica
[src]
x1 = 69.7948942333879
x2 = -40.1608486422549
x3 = 44.6621530046695
x4 = -71.5767751781528
x5 = 88.6444501549266
x6 = 22.671004429541
x7 = 54.0869309654389
x8 = 57.2285236190287
x9 = 66.6533015797981
x10 = -65.2935898709732
x11 = -68.435182524563
x12 = -62.1519972173834
x13 = 0.679855854412419
x14 = -24.4528853743059
x15 = -2251.84207676947
x16 = -55.8688119102039
x17 = -51.7665196125301
x18 = -46.4440339494345
x19 = -84.143145792512
x20 = -30.7360706814855
x21 = -73.7576681876586
x22 = 76.0780795405675
x23 = 32.0957823903104
x24 = -33.8776633350753
x25 = 17050.1031868862
x26 = 47.8037456582593
x27 = -5.60332945276717
x28 = 82.361264847747
x29 = -99.851109060461
x30 = -27.5944780278957
x31 = 958.865615199299
x32 = -59.0104045637936
x33 = 204.883378337749
x34 = 98.069228115696
x35 = 6.96304116159201
x36 = 110.635598730055
x37 = -90.4263310996916
x38 = 19.5294117759512
x39 = 85.5028575013368
x40 = -52.7272192566141
x41 = 41.5205603510797
x42 = -18.1697000671263
x43 = 35.2373750439001
x44 = 25.8125970831308
x45 = 38.3789676974899
x46 = -77.8599604853324
x47 = 79.2196721941573
x48 = 226.874526912878
x49 = 94.9276354621062
x50 = -49.5856266030243
x51 = -93.5679237532814
x52 = 179.750637109031
x53 = 13.2462264687716
x54 = 60.3701162726185
x55 = -2.46173679917737
x56 = -81.0015531389222
x57 = 10.1046338151818
x58 = 91.7860428085164
x59 = -8.74492210635696
x60 = 63.5117089262083
x61 = 314.839121213392
x62 = -11.8865147599468
x63 = 120.060376690825
x64 = 3.82144850800221
x65 = 16.3878191223614
x66 = -37.0192559886651
x66 = -37.0192559886651