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Expresiones con funciones
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2*cos^2(x)+sqrt(3)*sin(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 ___ 2*cos (x) + \/ 3 *sin(x) = 0
$$\sqrt{3} \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sqrt{3} \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)} = 0$$
cambiamos
$$\sqrt{3} \sin{\left(x \right)} + \cos{\left(2 x \right)} + 1 = 0$$
$$- 2 \sin^{2}{\left(x \right)} + \sqrt{3} \sin{\left(x \right)} + 2 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -2$$
$$b = \sqrt{3}$$
$$c = 2$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = - \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4}$$
$$w_{2} = \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)}$$
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)} + \pi$$
$$x_{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$\sqrt{3} \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)} = 0$$
cambiamos
$$\sqrt{3} \sin{\left(x \right)} + \cos{\left(2 x \right)} + 1 = 0$$
$$- 2 \sin^{2}{\left(x \right)} + \sqrt{3} \sin{\left(x \right)} + 2 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -2$$
$$b = \sqrt{3}$$
$$c = 2$$
, entonces
D = b^2 - 4 * a * c =
(sqrt(3))^2 - 4 * (-2) * (2) = 19
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = - \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4}$$
$$w_{2} = \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)}$$
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)} + \pi$$
$$x_{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
Suma y producto de raíces
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suma
/ / ____________\\ / / ____________\\ / / ____________\\ / / ____________\\ / ____________\ / ____________\
| | ____ ___ ___ / ____ || | | ____ ___ ___ / ____ || | | ___ ____ ___ / ____ || | | ___ ____ ___ / ____ || | ___ ____ ___ / ____ | | ___ ____ ___ / ____ |
| | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 |
- 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|| + 2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------|| - 2*atan|----- + ------ + ---------------------| - 2*atan|----- + ------ - ---------------------|
\ \ 4 4 4 // \ \ 4 4 4 // \ \ 4 4 4 // \ \ 4 4 4 // \ 4 4 4 / \ 4 4 4 /
$$- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} + \left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right)\right)\right)$$
=
/ ____________\ / ____________\ / / ____________\\ / / ____________\\ / / ____________\\ / / ____________\\
| ___ ____ ___ / ____ | | ___ ____ ___ / ____ | | | ____ ___ ___ / ____ || | | ___ ____ ___ / ____ || | | ____ ___ ___ / ____ || | | ___ ____ ___ / ____ ||
|\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 ||
- 2*atan|----- + ------ - ---------------------| - 2*atan|----- + ------ + ---------------------| - 2*re|atan|- ------ + ----- + ---------------------|| + 2*re|atan|- ----- + ------ + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------||
\ 4 4 4 / \ 4 4 4 / \ \ 4 4 4 // \ \ 4 4 4 // \ \ 4 4 4 // \ \ 4 4 4 //
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}$$
producto
/ / / ____________\\ / / ____________\\\ / / / ____________\\ / / ____________\\\ / ____________\ / ____________\ | | | ____ ___ ___ / ____ || | | ____ ___ ___ / ____ ||| | | | ___ ____ ___ / ____ || | | ___ ____ ___ / ____ ||| | ___ ____ ___ / ____ | | ___ ____ ___ / ____ | | | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 ||| | | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 ||| |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | |- 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|||*|2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------|||*-2*atan|----- + ------ + ---------------------|*-2*atan|----- + ------ - ---------------------| \ \ \ 4 4 4 // \ \ 4 4 4 /// \ \ \ 4 4 4 // \ \ 4 4 4 /// \ 4 4 4 / \ 4 4 4 /
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}\right)$$
=
/ / / ____________\\ / / ____________\\\ / / / ____________\\ / / ____________\\\ / ____________\ / ____________\
| | | ___ ____ ___ / ____ || | | ___ ____ ___ / ____ ||| | | | ____ ___ ___ / ____ || | | ____ ___ ___ / ____ ||| | ___ ____ ___ / ____ | | ___ ____ ___ / ____ |
| | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 ||| | | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 ||| |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 | |\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 |
-16*|I*im|atan|- ----- + ------ + ---------------------|| + re|atan|- ----- + ------ + ---------------------|||*|I*im|atan|- ------ + ----- + ---------------------|| + re|atan|- ------ + ----- + ---------------------|||*atan|----- + ------ - ---------------------|*atan|----- + ------ + ---------------------|
\ \ \ 4 4 4 // \ \ 4 4 4 /// \ \ \ 4 4 4 // \ \ 4 4 4 /// \ 4 4 4 / \ 4 4 4 /
$$- 16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
-16*(i*im(atan(-sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)) + re(atan(-sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)))*(i*im(atan(-sqrt(19)/4 + sqrt(3)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)) + re(atan(-sqrt(19)/4 + sqrt(3)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)))*atan(sqrt(3)/4 + sqrt(19)/4 - sqrt(2)*sqrt(3 + sqrt(57))/4)*atan(sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 + sqrt(57))/4)
Respuesta rápida
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/ / ____________\\ / / ____________\\
| | ____ ___ ___ / ____ || | | ____ ___ ___ / ____ ||
| | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 || | | \/ 19 \/ 3 \/ 2 *\/ 3 - \/ 57 ||
x1 = - 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------||
\ \ 4 4 4 // \ \ 4 4 4 //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}$$
/ / ____________\\ / / ____________\\
| | ___ ____ ___ / ____ || | | ___ ____ ___ / ____ ||
| | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 || | | \/ 3 \/ 19 \/ 2 *\/ 3 - \/ 57 ||
x2 = 2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------||
\ \ 4 4 4 // \ \ 4 4 4 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}$$
/ ____________\
| ___ ____ ___ / ____ |
|\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 |
x3 = -2*atan|----- + ------ + ---------------------|
\ 4 4 4 /
$$x_{3} = - 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)}$$
/ ____________\
| ___ ____ ___ / ____ |
|\/ 3 \/ 19 \/ 2 *\/ 3 + \/ 57 |
x4 = -2*atan|----- + ------ - ---------------------|
\ 4 4 4 /
$$x_{4} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}$$
x4 = -2*atan(-sqrt(2)*sqrt(3 + sqrt(57))/4 + sqrt(3)/4 + sqrt(19)/4)
Respuesta numérica
[src]
x1 = 36.9826612839022
x2 = 74.6817731269797
x3 = -82.39785955251
x4 = 24.416290669543
x5 = 54.1235256702018
x6 = 99.814514355698
x7 = -50.981933016612
x8 = -84.1065510877491
x9 = -90.3897363949286
x10 = -44.6987477094325
x11 = -71.5401804733899
x12 = -38.4155624022529
x13 = -63.5483036309712
x14 = -46.4074392446715
x15 = -27.5578833231328
x16 = 28.9907844414835
x17 = 68.3985878198001
x18 = 16.4244138271243
x19 = 35.2739697486631
x20 = -6939.06172122068
x21 = 30.6994759767226
x22 = -33.8410686303124
x23 = -76.1146742453304
x24 = 41.5571550558427
x25 = -96.6729217021082
x26 = -57.2651183237916
x27 = 18.1331053623634
x28 = 93.5313290485184
x29 = -52.6906245518511
x30 = -13.2828211735345
x31 = -88.6810448596896
x32 = 85.5394522060998
x33 = 43.2658465910818
x34 = 10.1412285199447
x35 = 91.8226375132794
x36 = 11.8499200551838
x37 = -32.1323770950733
x38 = 5.56673474800423
x39 = -101.247415474049
x40 = -58.9738098590307
x41 = 55.8322172054409
x42 = 22.7075991343039
x43 = -65.2569951662103
x44 = 47.8403403630222
x45 = 3.85804321276515
x46 = 60.4067109773814
x47 = -19.5660064807141
x48 = 79.2562668989202
x49 = 72.9730815917406
x50 = 49.5490318982613
x51 = 87.2481437413389
x52 = -25.8491917878937
x53 = 80.9649584341593
x54 = -77.8233657805695
x55 = -94.9642301668692
x56 = 98.1058228204589
x57 = -69.8314889381508
x58 = -8.70832740159403
x59 = -0.716450559175354
x60 = -6.99963586635494
x61 = 66.689896284561
x62 = 62.1154025126205
x63 = -2.42514209441444
x64 = -40.124253937492
x65 = -21.2746980159532
x65 = -21.2746980159532