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- La ecuación:
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Ecuación x^2+5x=36
-
Ecuación 3*x=8
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
-
Expresiones idénticas
- (diecinueve / cincuenta)^ tres *x^ tres + diecinueve * dos *(diecinueve / cincuenta)^ tres *x^ dos / cincuenta - treinta y siete * treinta y cuatro mil quinientos setenta y siete /(diez * cien * diez ^ tres * cinco / ocho)= cero
- (19 dividir por 50) al cubo multiplicar por x al cubo más 19 multiplicar por 2 multiplicar por (19 dividir por 50) al cubo multiplicar por x al cuadrado dividir por 50 menos 37 multiplicar por 34577 dividir por (10 multiplicar por 100 multiplicar por 10 al cubo multiplicar por 5 dividir por 8) es igual a 0
- (diecinueve dividir por cincuenta) en el grado tres multiplicar por x en el grado tres más diecinueve multiplicar por dos multiplicar por (diecinueve dividir por cincuenta) en el grado tres multiplicar por x en el grado dos dividir por cincuenta menos treinta y siete multiplicar por treinta y cuatro mil quinientos setenta y siete dividir por (diez multiplicar por cien multiplicar por diez en el grado tres multiplicar por cinco dividir por ocho) es igual a cero
- (19/50)3*x3+19*2*(19/50)3*x2/50-37*34577/(10*100*103*5/8)=0
- 19/503*x3+19*2*19/503*x2/50-37*34577/10*100*103*5/8=0
- (19/50)³*x³+19*2*(19/50)³*x²/50-37*34577/(10*100*10³*5/8)=0
- (19/50) en el grado 3*x en el grado 3+19*2*(19/50) en el grado 3*x en el grado 2/50-37*34577/(10*100*10 en el grado 3*5/8)=0
- (19/50)^3x^3+192(19/50)^3x^2/50-3734577/(1010010^35/8)=0
- (19/50)3x3+192(19/50)3x2/50-3734577/(101001035/8)=0
- 19/503x3+19219/503x2/50-3734577/101001035/8=0
- 19/50^3x^3+19219/50^3x^2/50-3734577/1010010^35/8=0
- (19/50)^3*x^3+19*2*(19/50)^3*x^2/50-37*34577/(10*100*10^3*5/8)=O
- (19 dividir por 50)^3*x^3+19*2*(19 dividir por 50)^3*x^2 dividir por 50-37*34577 dividir por (10*100*10^3*5 dividir por 8)=0
-
Expresiones semejantes
- (19/50)^3*x^3-19*2*(19/50)^3*x^2/50-37*34577/(10*100*10^3*5/8)=0
- (19/50)^3*x^3+19*2*(19/50)^3*x^2/50+37*34577/(10*100*10^3*5/8)=0
(19/50)^3*x^3+19*2*(19/50)^3*x^2/50-37*34577/(10*100*10^3*5/8)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3
/19\ 2
3 38*|--| *x
/19\ 3 \50/ 1279349
|--| *x + ----------- - ----------- = 0
\50/ 50 /5*1000000\
|---------|
\ 8 /
$$\left(\left(\frac{19}{50}\right)^{3} x^{3} + \frac{38 \left(\frac{19}{50}\right)^{3} x^{2}}{50}\right) - \frac{1279349}{\frac{5}{8} \cdot 1000000} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(\left(\frac{19}{50}\right)^{3} x^{3} + \frac{38 \left(\frac{19}{50}\right)^{3} x^{2}}{50}\right) - \frac{1279349}{\frac{5}{8} \cdot 1000000} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{19 x^{2}}{25} - \frac{1279349}{34295} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{19}{25}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{1279349}{34295}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{19}{25}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = - \frac{1279349}{34295}$$
$$\left(\left(\frac{19}{50}\right)^{3} x^{3} + \frac{38 \left(\frac{19}{50}\right)^{3} x^{2}}{50}\right) - \frac{1279349}{\frac{5}{8} \cdot 1000000} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{19 x^{2}}{25} - \frac{1279349}{34295} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{19}{25}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{1279349}{34295}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{19}{25}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = - \frac{1279349}{34295}$$
Suma y producto de raíces
[src]
suma
________________________________________ / ________________________________________ \ ________________________________________ / ________________________________________ \
/ _____________________ | / _____________________ | / _____________________ | / _____________________ |
/ 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 | ________________________________________
3 / ------------ + ----------------------- | \/ 3 *3 / ------------ + ----------------------- ___ | 3 / ------------ + ----------------------- |\/ 3 *3 / ------------ + ----------------------- ___ | / _____________________
19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 | 19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 | 19 / 107850980113 \/ 2067880010324452485 361
- -- - --------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + ---------------------------------------------------| + - -- - --------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - ---------------------------------------------------| + - -- + 3 / ------------ + ----------------------- + --------------------------------------------------
75 ________________________________________ 2 | 2 ________________________________________| 75 ________________________________________ 2 | 2 ________________________________________| 75 \/ 5787281250 77163750 ________________________________________
/ _____________________ | / _____________________ | / _____________________ | / _____________________ | / _____________________
/ 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485
11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- | 5625*3 / ------------ + -----------------------
\/ 5787281250 77163750 \ \/ 5787281250 77163750 / \/ 5787281250 77163750 \ \/ 5787281250 77163750 / \/ 5787281250 77163750
$$\left(- \frac{19}{75} + \frac{361}{5625 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} + \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2}\right)\right)\right)$$
=
/ ________________________________________ \ / ________________________________________ \
| / _____________________ | | / _____________________ |
| ___ / 107850980113 \/ 2067880010324452485 | | ___ / 107850980113 \/ 2067880010324452485 |
|\/ 3 *3 / ------------ + ----------------------- ___ | | \/ 3 *3 / ------------ + ----------------------- ___ |
19 | \/ 5787281250 77163750 361*\/ 3 | | \/ 5787281250 77163750 361*\/ 3 |
- -- + I*|--------------------------------------------------- - ---------------------------------------------------| + I*|- --------------------------------------------------- + ---------------------------------------------------|
25 | 2 ________________________________________| | 2 ________________________________________|
| / _____________________ | | / _____________________ |
| / 107850980113 \/ 2067880010324452485 | | / 107850980113 \/ 2067880010324452485 |
| 11250*3 / ------------ + ----------------------- | | 11250*3 / ------------ + ----------------------- |
\ \/ 5787281250 77163750 / \ \/ 5787281250 77163750 /
$$- \frac{19}{25} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} + \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}\right) + i \left(- \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2}\right)$$
producto
/ ________________________________________ / ________________________________________ \\ / ________________________________________ / ________________________________________ \\ | / _____________________ | / _____________________ || | / _____________________ | / _____________________ || | / 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 || | / 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 || / ________________________________________ \ | 3 / ------------ + ----------------------- | \/ 3 *3 / ------------ + ----------------------- ___ || | 3 / ------------ + ----------------------- |\/ 3 *3 / ------------ + ----------------------- ___ || | / _____________________ | | 19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 || | 19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 || | 19 / 107850980113 \/ 2067880010324452485 361 | |- -- - --------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + ---------------------------------------------------||*|- -- - --------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - ---------------------------------------------------||*|- -- + 3 / ------------ + ----------------------- + --------------------------------------------------| | 75 ________________________________________ 2 | 2 ________________________________________|| | 75 ________________________________________ 2 | 2 ________________________________________|| | 75 \/ 5787281250 77163750 ________________________________________| | / _____________________ | / _____________________ || | / _____________________ | / _____________________ || | / _____________________ | | / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 || | / 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 || | / 107850980113 \/ 2067880010324452485 | | 11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- || | 11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- || | 5625*3 / ------------ + ----------------------- | \ \/ 5787281250 77163750 \ \/ 5787281250 77163750 // \ \/ 5787281250 77163750 \ \/ 5787281250 77163750 // \ \/ 5787281250 77163750 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} + \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}\right)\right) \left(- \frac{19}{75} + \frac{361}{5625 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}\right)$$
=
1279349 ------- 34295
$$\frac{1279349}{34295}$$
1279349/34295
Respuesta rápida
[src]
________________________________________ / ________________________________________ \
/ _____________________ | / _____________________ |
/ 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 |
3 / ------------ + ----------------------- | \/ 3 *3 / ------------ + ----------------------- ___ |
19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 |
x1 = - -- - --------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + ---------------------------------------------------|
75 ________________________________________ 2 | 2 ________________________________________|
/ _____________________ | / _____________________ |
/ 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 |
11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- |
\/ 5787281250 77163750 \ \/ 5787281250 77163750 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} + \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}\right)$$
________________________________________ / ________________________________________ \
/ _____________________ | / _____________________ |
/ 107850980113 \/ 2067880010324452485 | ___ / 107850980113 \/ 2067880010324452485 |
3 / ------------ + ----------------------- |\/ 3 *3 / ------------ + ----------------------- ___ |
19 361 \/ 5787281250 77163750 | \/ 5787281250 77163750 361*\/ 3 |
x2 = - -- - --------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - ---------------------------------------------------|
75 ________________________________________ 2 | 2 ________________________________________|
/ _____________________ | / _____________________ |
/ 107850980113 \/ 2067880010324452485 | / 107850980113 \/ 2067880010324452485 |
11250*3 / ------------ + ----------------------- | 11250*3 / ------------ + ----------------------- |
\/ 5787281250 77163750 \ \/ 5787281250 77163750 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2} - \frac{19}{75} - \frac{361}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + i \left(- \frac{361 \sqrt{3}}{11250 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}}{2}\right)$$
________________________________________
/ _____________________
19 / 107850980113 \/ 2067880010324452485 361
x3 = - -- + 3 / ------------ + ----------------------- + --------------------------------------------------
75 \/ 5787281250 77163750 ________________________________________
/ _____________________
/ 107850980113 \/ 2067880010324452485
5625*3 / ------------ + -----------------------
\/ 5787281250 77163750
$$x_{3} = - \frac{19}{75} + \frac{361}{5625 \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}} + \sqrt[3]{\frac{\sqrt{2067880010324452485}}{77163750} + \frac{107850980113}{5787281250}}$$
x3 = -19/75 + 361/(5625*(sqrt(2067880010324452485)/77163750 + 107850980113/5787281250)^(1/3)) + (sqrt(2067880010324452485)/77163750 + 107850980113/5787281250)^(1/3)
Respuesta numérica
[src]
x1 = -1.9331192361471 + 2.87619691685779*i
x2 = 3.1062384722942
x3 = -1.9331192361471 - 2.87619691685779*i
x3 = -1.9331192361471 - 2.87619691685779*i