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- La ecuación:
-
Ecuación x^2-4x+5=0
-
Ecuación x^2+3x+2=0
-
Ecuación x^2+3x=4
-
Ecuación -x^2+5*x-6=0
- Expresar {x} en función de y en la ecuación:
- 10*x-2*y=0
- 1*x+4*y=20
- 3*x-7*y=13
- 13*x-15*y=-6
-
Expresiones idénticas
- uno -tg(x)^ dos =-(tg(x)-5ctg(x))*tg(2x)
- 1 menos tg(x) al cuadrado es igual a menos (tg(x) menos 5ctg(x)) multiplicar por tg(2x)
- uno menos tg(x) en el grado dos es igual a menos (tg(x) menos 5ctg(x)) multiplicar por tg(2x)
- 1-tg(x)2=-(tg(x)-5ctg(x))*tg(2x)
- 1-tgx2=-tgx-5ctgx*tg2x
- 1-tg(x)²=-(tg(x)-5ctg(x))*tg(2x)
- 1-tg(x) en el grado 2=-(tg(x)-5ctg(x))*tg(2x)
- 1-tg(x)^2=-(tg(x)-5ctg(x))tg(2x)
- 1-tg(x)2=-(tg(x)-5ctg(x))tg(2x)
- 1-tgx2=-tgx-5ctgxtg2x
- 1-tgx^2=-tgx-5ctgxtg2x
-
Expresiones semejantes
- 1+tg(x)^2=-(tg(x)-5ctg(x))*tg(2x)
- 1-tg(x)^2=-(tg(x)+5ctg(x))*tg(2x)
- 1-tg(x)^2=+(tg(x)-5ctg(x))*tg(2x)
-
Expresiones con funciones
- tg
- tg(x)=-3
- tg(x)=-1/2
- tg(x)=2
- tg(x)=-4
- tg=p/5
- tg
- tg(x)=-3
- tg(x)=-1/2
- tg(x)=2
- tg(x)=-4
- tg=p/5
- tg
- tg(x)=-3
- tg(x)=-1/2
- tg(x)=2
- tg(x)=-4
- tg=p/5
1-tg(x)^2=-(tg(x)-5ctg(x))*tg(2x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 1 - tan (x) = (-tan(x) + 5*cot(x))*tan(2*x)
$$1 - \tan^{2}{\left(x \right)} = \left(- \tan{\left(x \right)} + 5 \cot{\left(x \right)}\right) \tan{\left(2 x \right)}$$
Suma y producto de raíces
[src]
suma
/ ___\ / ___\ / ___\ / ___\ 2*pi pi pi 2*pi pi I*log\2 - \/ 3 / pi I*log\2 + \/ 3 / pi I*log\2 - \/ 3 / pi I*log\2 + \/ 3 / - ---- - -- + -- + ---- + - -- - ---------------- + - -- - ---------------- + -- - ---------------- + -- - ---------------- 3 3 3 3 2 2 2 2 2 2 2 2
$$\left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(\left(- \frac{2 \pi}{3} - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \frac{2 \pi}{3}\right) + \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)\right) + \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)$$
=
/ ___\ / ___\ - I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$
producto
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ -2*pi -pi pi 2*pi | pi I*log\2 - \/ 3 /| | pi I*log\2 + \/ 3 /| |pi I*log\2 - \/ 3 /| |pi I*log\2 + \/ 3 /| -----*----*--*----*|- -- - ----------------|*|- -- - ----------------|*|-- - ----------------|*|-- - ----------------| 3 3 3 3 \ 2 2 / \ 2 2 / \2 2 / \2 2 /
$$\frac{2 \pi}{3} \frac{\pi}{3} \cdot - \frac{2 \pi}{3} \left(- \frac{\pi}{3}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right)$$
=
4 / / ___\\ / / ___\\ / / ___\\ / / ___\\
pi *\pi + I*log\2 + \/ 3 //*\pi + I*log\2 - \/ 3 //*\pi - I*log\2 + \/ 3 //*\pi - I*log\2 - \/ 3 //
---------------------------------------------------------------------------------------------------
324
$$\frac{\pi^{4} \left(\pi - i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi + i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi - i \log{\left(\sqrt{3} + 2 \right)}\right) \left(\pi + i \log{\left(\sqrt{3} + 2 \right)}\right)}{324}$$
pi^4*(pi + i*log(2 + sqrt(3)))*(pi + i*log(2 - sqrt(3)))*(pi - i*log(2 + sqrt(3)))*(pi - i*log(2 - sqrt(3)))/324
Respuesta rápida
[src]
-2*pi
x1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
-pi
x2 = ----
3
$$x_{2} = - \frac{\pi}{3}$$
pi
x3 = --
3
$$x_{3} = \frac{\pi}{3}$$
2*pi
x4 = ----
3
$$x_{4} = \frac{2 \pi}{3}$$
/ ___\
pi I*log\2 - \/ 3 /
x5 = - -- - ----------------
2 2
$$x_{5} = - \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$
/ ___\
pi I*log\2 + \/ 3 /
x6 = - -- - ----------------
2 2
$$x_{6} = - \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$
/ ___\
pi I*log\2 - \/ 3 /
x7 = -- - ----------------
2 2
$$x_{7} = \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$
/ ___\
pi I*log\2 + \/ 3 /
x8 = -- - ----------------
2 2
$$x_{8} = \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$
x8 = pi/2 - i*log(sqrt(3) + 2)/2
Respuesta numérica
[src]
x1 = 49.2182849062401
x2 = 90.0589894029074
x3 = -38.7463093942741
x4 = -39.7935069454707
x5 = -48.1710873550435
x6 = 35.6047167406843
x7 = -80.634211442138
x8 = -105.766952670856
x9 = -61.7846555205993
x10 = 45.0294947014537
x11 = -74.3510261349584
x12 = 70.162235930172
x13 = -83.7758040957278
x14 = -93.2005820564972
x15 = 4.18879020478639
x16 = -13.6135681655558
x17 = -68.0678408277789
x18 = -52.3598775598299
x19 = -79.5870138909414
x20 = 52.3598775598299
x21 = 33.5103216382911
x22 = 86.9173967493176
x23 = -19.8967534727354
x24 = 13.6135681655558
x25 = 27.2271363311115
x26 = 80.634211442138
x27 = -58.6430628670095
x28 = -85.870199198121
x29 = 96.342174710087
x30 = -41128.6838232464
x31 = -63.8790506229925
x32 = -10.471975511966
x33 = 24.0855436775217
x34 = 58.6430628670095
x35 = 30.3687289847013
x36 = 92.1533845053006
x37 = -24.0855436775217
x38 = -8.37758040957278
x39 = -101.57816246607
x40 = -35.6047167406843
x41 = 39.7935069454707
x42 = 74.3510261349584
x43 = 26.1799387799149
x44 = -274.365758413509
x45 = 48.1710873550435
x46 = 8.37758040957278
x47 = 359.188760060433
x48 = 63.8790506229925
x49 = 164.410015537866
x50 = -41.8879020478639
x51 = -17.8023583703422
x52 = -98.4365698124802
x53 = -2.0943951023932
x54 = -90.0589894029074
x55 = 170.693200845045
x56 = -57.5958653158129
x57 = 68.0678408277789
x58 = 2.0943951023932
x59 = -30.3687289847013
x60 = -96.342174710087
x61 = 41.8879020478639
x62 = 46.0766922526503
x63 = 85.870199198121
x64 = 19.8967534727354
x65 = 670.206432765823
x66 = -5734.45379035257
x67 = -70.162235930172
x68 = -46.0766922526503
x68 = -46.0766922526503