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- La ecuación:
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Ecuación x^2-x-6=6
-
Ecuación 3*x^2+21*x=0
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Ecuación 4/x=x+3
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Ecuación -2x=3
- Expresar {x} en función de y en la ecuación:
- -8*x+16*y=11
- -11*x+4*y=-20
- -14*x+12*y=-6
- 10*x-18*y=-6
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Expresiones idénticas
- cinco (x+ dos)-(dos - tres x^3)=(dos x- uno)(9x^2+3x+ uno)-(2x- uno)(27x- uno)
- 5(x más 2) menos (2 menos 3x al cubo ) es igual a (2x menos 1)(9x al cuadrado más 3x más 1) menos (2x menos 1)(27x menos 1)
- cinco (x más dos) menos (dos menos tres x al cubo ) es igual a (dos x menos uno)(9x al cuadrado más 3x más uno) menos (2x menos uno)(27x menos uno)
- 5(x+2)-(2-3x3)=(2x-1)(9x2+3x+1)-(2x-1)(27x-1)
- 5x+2-2-3x3=2x-19x2+3x+1-2x-127x-1
- 5(x+2)-(2-3x³)=(2x-1)(9x²+3x+1)-(2x-1)(27x-1)
- 5(x+2)-(2-3x en el grado 3)=(2x-1)(9x en el grado 2+3x+1)-(2x-1)(27x-1)
- 5x+2-2-3x^3=2x-19x^2+3x+1-2x-127x-1
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Expresiones semejantes
- 5(x+2)-(2-3x^3)=(2x+1)(9x^2+3x+1)-(2x-1)(27x-1)
- 5(x-2)-(2-3x^3)=(2x-1)(9x^2+3x+1)-(2x-1)(27x-1)
- 5(x+2)-(2-3x^3)=(2x-1)(9x^2+3x+1)+(2x-1)(27x-1)
- 5(x+2)-(2-3x^3)=(2x-1)(9x^2+3x+1)-(2x-1)(27x+1)
- 5(x+2)+(2-3x^3)=(2x-1)(9x^2+3x+1)-(2x-1)(27x-1)
- 5(x+2)-(2-3x^3)=(2x-1)(9x^2+3x-1)-(2x-1)(27x-1)
- 5(x+2)-(2+3x^3)=(2x-1)(9x^2+3x+1)-(2x-1)(27x-1)
- 5(x+2)-(2-3x^3)=(2x-1)(9x^2+3x+1)-(2x+1)(27x-1)
- 5(x+2)-(2-3x^3)=(2x-1)(9x^2-3x+1)-(2x-1)(27x-1)
5(x+2)-(2-3x^3)=(2x-1)(9x^2+3x+1)-(2x-1)(27x-1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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3 / 2 \ 5*(x + 2) + -2 + 3*x = (2*x - 1)*\9*x + 3*x + 1/ - (2*x - 1)*(27*x - 1)
$$5 \left(x + 2\right) + \left(3 x^{3} - 2\right) = - \left(2 x - 1\right) \left(27 x - 1\right) + \left(2 x - 1\right) \left(\left(9 x^{2} + 3 x\right) + 1\right)$$
Suma y producto de raíces
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suma
____________________ / ____________________ \ ____________________ / ____________________ \
/ _________ | / _________ | / _________ | / _________ |
/ 9413 \/ 1162273 | ___ / 9413 \/ 1162273 | / 9413 \/ 1162273 | ___ / 9413 \/ 1162273 | ____________________
3 / ---- + ----------- | \/ 3 *3 / ---- + ----------- ___ | 3 / ---- + ----------- |\/ 3 *3 / ---- + ----------- ___ | / _________
19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 | 19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 | 19 / 9413 \/ 1162273 82
-- - ---------------------------- - ------------------------- + I*|- ------------------------------- + ----------------------------| + -- - ---------------------------- - ------------------------- + I*|------------------------------- - ----------------------------| + -- + 3 / ---- + ----------- + ----------------------------
15 ____________________ 2 | 2 ____________________| 15 ____________________ 2 | 2 ____________________| 15 \/ 6750 1350 ____________________
/ _________ | / _________ | / _________ | / _________ | / _________
/ 9413 \/ 1162273 | / 9413 \/ 1162273 | / 9413 \/ 1162273 | / 9413 \/ 1162273 | / 9413 \/ 1162273
75*3 / ---- + ----------- | 75*3 / ---- + ----------- | 75*3 / ---- + ----------- | 75*3 / ---- + ----------- | 75*3 / ---- + -----------
\/ 6750 1350 \ \/ 6750 1350 / \/ 6750 1350 \ \/ 6750 1350 / \/ 6750 1350
$$\left(\frac{82}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} + \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2}\right)\right)\right)$$
=
/ ____________________ \ / ____________________ \
| / _________ | | / _________ |
| ___ / 9413 \/ 1162273 | | ___ / 9413 \/ 1162273 |
|\/ 3 *3 / ---- + ----------- ___ | | \/ 3 *3 / ---- + ----------- ___ |
19 | \/ 6750 1350 41*\/ 3 | | \/ 6750 1350 41*\/ 3 |
-- + I*|------------------------------- - ----------------------------| + I*|- ------------------------------- + ----------------------------|
5 | 2 ____________________| | 2 ____________________|
| / _________ | | / _________ |
| / 9413 \/ 1162273 | | / 9413 \/ 1162273 |
| 75*3 / ---- + ----------- | | 75*3 / ---- + ----------- |
\ \/ 6750 1350 / \ \/ 6750 1350 /
$$\frac{19}{5} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} + \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}\right) + i \left(- \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2}\right)$$
producto
/ ____________________ / ____________________ \\ / ____________________ / ____________________ \\ | / _________ | / _________ || | / _________ | / _________ || | / 9413 \/ 1162273 | ___ / 9413 \/ 1162273 || | / 9413 \/ 1162273 | ___ / 9413 \/ 1162273 || / ____________________ \ | 3 / ---- + ----------- | \/ 3 *3 / ---- + ----------- ___ || | 3 / ---- + ----------- |\/ 3 *3 / ---- + ----------- ___ || | / _________ | |19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 || |19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 || |19 / 9413 \/ 1162273 82 | |-- - ---------------------------- - ------------------------- + I*|- ------------------------------- + ----------------------------||*|-- - ---------------------------- - ------------------------- + I*|------------------------------- - ----------------------------||*|-- + 3 / ---- + ----------- + ----------------------------| |15 ____________________ 2 | 2 ____________________|| |15 ____________________ 2 | 2 ____________________|| |15 \/ 6750 1350 ____________________| | / _________ | / _________ || | / _________ | / _________ || | / _________ | | / 9413 \/ 1162273 | / 9413 \/ 1162273 || | / 9413 \/ 1162273 | / 9413 \/ 1162273 || | / 9413 \/ 1162273 | | 75*3 / ---- + ----------- | 75*3 / ---- + ----------- || | 75*3 / ---- + ----------- | 75*3 / ---- + ----------- || | 75*3 / ---- + ----------- | \ \/ 6750 1350 \ \/ 6750 1350 // \ \/ 6750 1350 \ \/ 6750 1350 // \ \/ 6750 1350 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} + \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}\right)\right) \left(\frac{82}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}\right)$$
=
2/3
$$\frac{2}{3}$$
2/3
Respuesta rápida
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____________________ / ____________________ \
/ _________ | / _________ |
/ 9413 \/ 1162273 | ___ / 9413 \/ 1162273 |
3 / ---- + ----------- | \/ 3 *3 / ---- + ----------- ___ |
19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 |
x1 = -- - ---------------------------- - ------------------------- + I*|- ------------------------------- + ----------------------------|
15 ____________________ 2 | 2 ____________________|
/ _________ | / _________ |
/ 9413 \/ 1162273 | / 9413 \/ 1162273 |
75*3 / ---- + ----------- | 75*3 / ---- + ----------- |
\/ 6750 1350 \ \/ 6750 1350 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} + \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}\right)$$
____________________ / ____________________ \
/ _________ | / _________ |
/ 9413 \/ 1162273 | ___ / 9413 \/ 1162273 |
3 / ---- + ----------- |\/ 3 *3 / ---- + ----------- ___ |
19 41 \/ 6750 1350 | \/ 6750 1350 41*\/ 3 |
x2 = -- - ---------------------------- - ------------------------- + I*|------------------------------- - ----------------------------|
15 ____________________ 2 | 2 ____________________|
/ _________ | / _________ |
/ 9413 \/ 1162273 | / 9413 \/ 1162273 |
75*3 / ---- + ----------- | 75*3 / ---- + ----------- |
\/ 6750 1350 \ \/ 6750 1350 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2} - \frac{41}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + i \left(- \frac{41 \sqrt{3}}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}}{2}\right)$$
____________________
/ _________
19 / 9413 \/ 1162273 82
x3 = -- + 3 / ---- + ----------- + ----------------------------
15 \/ 6750 1350 ____________________
/ _________
/ 9413 \/ 1162273
75*3 / ---- + -----------
\/ 6750 1350
$$x_{3} = \frac{82}{75 \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}} + \frac{19}{15} + \sqrt[3]{\frac{\sqrt{1162273}}{1350} + \frac{9413}{6750}}$$
x3 = 82/(75*(sqrt(1162273)/1350 + 9413/6750)^(1/3)) + 19/15 + (sqrt(1162273)/1350 + 9413/6750)^(1/3)
Respuesta numérica
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x1 = 3.40742099637394
x2 = 0.196289501813032 - 0.396385954746523*i
x3 = 0.196289501813032 + 0.396385954746523*i
x3 = 0.196289501813032 + 0.396385954746523*i