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Ecuación 2*x^2+6*x+9=0
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Ecuación sin(x/4)=1/2
- Expresar {x} en función de y en la ecuación:
- 10*x+5*y=-17
- 16*x-17*y=-9
- -10*x+16*y=-6
- 10*x+7*y=9
-
Expresiones idénticas
- - dieciséis *(x^ tres)-(veinticinco . cuarenta y seis *x)- veinte mil setecientos setenta y cinco . tres = cero
- menos 16 multiplicar por (x al cubo ) menos (25.46 multiplicar por x) menos 20775.3 es igual a 0
- menos dieciséis multiplicar por (x en el grado tres) menos (veinticinco . cuarenta y seis multiplicar por x) menos veinte mil setecientos setenta y cinco . tres es igual a cero
- -16*(x3)-(25.46*x)-20775.3=0
- -16*x3-25.46*x-20775.3=0
- -16*(x³)-(25.46*x)-20775.3=0
- -16*(x en el grado 3)-(25.46*x)-20775.3=0
- -16(x^3)-(25.46x)-20775.3=0
- -16(x3)-(25.46x)-20775.3=0
- -16x3-25.46x-20775.3=0
- -16x^3-25.46x-20775.3=0
- -16*(x^3)-(25.46*x)-20775.3=O
-
Expresiones semejantes
- 16*(x^3)-(25.46*x)-20775.3=0
- -16*(x^3)-(25.46*x)+20775.3=0
- -16*(x^3)+(25.46*x)-20775.3=0
-16*(x^3)-(25.46*x)-20775.3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 1273*x 207753
- 16*x - ------ - ------ = 0
50 10
$$\left(- 16 x^{3} - \frac{1273 x}{50}\right) - \frac{207753}{10} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 16 x^{3} - \frac{1273 x}{50}\right) - \frac{207753}{10} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{1273 x}{800} + \frac{207753}{160} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1273}{800}$$
$$v = \frac{d}{a}$$
$$v = \frac{207753}{160}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{1273}{800}$$
$$x_{1} x_{2} x_{3} = \frac{207753}{160}$$
$$\left(- 16 x^{3} - \frac{1273 x}{50}\right) - \frac{207753}{10} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{1273 x}{800} + \frac{207753}{160} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1273}{800}$$
$$v = \frac{d}{a}$$
$$v = \frac{207753}{160}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{1273}{800}$$
$$x_{1} x_{2} x_{3} = \frac{207753}{160}$$
Respuesta rápida
[src]
___________________________________ / ___________________________________ \
/ ___________________ | / ___________________ |
/ 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 |
3 / ------- + ----------------------- |\/ 3 *3 / ------- + ----------------------- ___ |
1273 \/ 320 32000 | \/ 320 32000 1273*\/ 3 |
x1 = - --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------|
___________________________________ 6 | 6 ___________________________________|
/ ___________________ | / ___________________ |
/ 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 |
1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- |
\/ 320 32000 \ \/ 320 32000 /
$$x_{1} = - \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)$$
___________________________________ / ___________________________________\
/ ___________________ | / ___________________ |
/ 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 |
3 / ------- + ----------------------- | ___ \/ 3 *3 / ------- + ----------------------- |
1273 \/ 320 32000 | 1273*\/ 3 \/ 320 32000 |
x2 = - --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------|
___________________________________ 6 | ___________________________________ 6 |
/ ___________________ | / ___________________ |
/ 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 |
1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- |
\/ 320 32000 \ \/ 320 32000 /
$$x_{2} = - \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)$$
___________________________________
/ ___________________
/ 5609331 3*\/ 34960672674890502
3 / ------- + -----------------------
\/ 320 32000 1273
x3 = - ---------------------------------------- + --------------------------------------------
3 ___________________________________
/ ___________________
/ 5609331 3*\/ 34960672674890502
800*3 / ------- + -----------------------
\/ 320 32000
$$x_{3} = - \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}$$
x3 = -(5609331/320 + 3*sqrt(34960672674890502)/32000)^(1/3)/3 + 1273/(800*(5609331/320 + 3*sqrt(34960672674890502)/32000)^(1/3))
Suma y producto de raíces
[src]
suma
___________________________________ / ___________________________________ \ ___________________________________ / ___________________________________\ ___________________________________
/ ___________________ | / ___________________ | / ___________________ | / ___________________ | / ___________________
/ 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502
3 / ------- + ----------------------- |\/ 3 *3 / ------- + ----------------------- ___ | 3 / ------- + ----------------------- | ___ \/ 3 *3 / ------- + ----------------------- | 3 / ------- + -----------------------
1273 \/ 320 32000 | \/ 320 32000 1273*\/ 3 | 1273 \/ 320 32000 | 1273*\/ 3 \/ 320 32000 | \/ 320 32000 1273
- --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------| + - --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------| + - ---------------------------------------- + --------------------------------------------
___________________________________ 6 | 6 ___________________________________| ___________________________________ 6 | ___________________________________ 6 | 3 ___________________________________
/ ___________________ | / ___________________ | / ___________________ | / ___________________ | / ___________________
/ 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502
1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- | 800*3 / ------- + -----------------------
\/ 320 32000 \ \/ 320 32000 / \/ 320 32000 \ \/ 320 32000 / \/ 320 32000
$$\left(- \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right) + \left(\left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)\right) + \left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)\right)\right)$$
=
/ ___________________________________\ / ___________________________________ \ | / ___________________ | | / ___________________ | | ___ / 5609331 3*\/ 34960672674890502 | | ___ / 5609331 3*\/ 34960672674890502 | | ___ \/ 3 *3 / ------- + ----------------------- | |\/ 3 *3 / ------- + ----------------------- ___ | | 1273*\/ 3 \/ 320 32000 | | \/ 320 32000 1273*\/ 3 | I*|- --------------------------------------------- - ----------------------------------------------| + I*|---------------------------------------------- + ---------------------------------------------| | ___________________________________ 6 | | 6 ___________________________________| | / ___________________ | | / ___________________ | | / 5609331 3*\/ 34960672674890502 | | / 5609331 3*\/ 34960672674890502 | | 1600*3 / ------- + ----------------------- | | 1600*3 / ------- + ----------------------- | \ \/ 320 32000 / \ \/ 320 32000 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right) + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)$$
producto
/ ___________________________________ / ___________________________________ \\ / ___________________________________ / ___________________________________\\ / ___________________________________ \ | / ___________________ | / ___________________ || | / ___________________ | / ___________________ || | / ___________________ | | / 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 || | / 5609331 3*\/ 34960672674890502 | ___ / 5609331 3*\/ 34960672674890502 || | / 5609331 3*\/ 34960672674890502 | | 3 / ------- + ----------------------- |\/ 3 *3 / ------- + ----------------------- ___ || | 3 / ------- + ----------------------- | ___ \/ 3 *3 / ------- + ----------------------- || | 3 / ------- + ----------------------- | | 1273 \/ 320 32000 | \/ 320 32000 1273*\/ 3 || | 1273 \/ 320 32000 | 1273*\/ 3 \/ 320 32000 || | \/ 320 32000 1273 | |- --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------||*|- --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------||*|- ---------------------------------------- + --------------------------------------------| | ___________________________________ 6 | 6 ___________________________________|| | ___________________________________ 6 | ___________________________________ 6 || | 3 ___________________________________| | / ___________________ | / ___________________ || | / ___________________ | / ___________________ || | / ___________________ | | / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 || | / 5609331 3*\/ 34960672674890502 | / 5609331 3*\/ 34960672674890502 || | / 5609331 3*\/ 34960672674890502 | | 1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- || | 1600*3 / ------- + ----------------------- | 1600*3 / ------- + ----------------------- || | 800*3 / ------- + ----------------------- | \ \/ 320 32000 \ \/ 320 32000 // \ \/ 320 32000 \ \/ 320 32000 // \ \/ 320 32000 /
$$\left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)\right) \left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)$$
=
-207753 -------- 160
$$- \frac{207753}{160}$$
-207753/160
Respuesta numérica
[src]
x1 = 5.43049405917003 - 9.49010259059632*i
x2 = -10.8609881183401
x3 = 5.43049405917003 + 9.49010259059632*i
x3 = 5.43049405917003 + 9.49010259059632*i