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- La ecuación:
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Ecuación x^2-4x+5=0
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Ecuación x^2+3x+2=0
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Ecuación -25-x=-17
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Ecuación x^2+3x=4
- 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
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Expresiones idénticas
- sesenta y uno . ochenta y siete - ocho . cinco *x^ dos - uno ocho x+ cuatro (x-1. seis)^ tres - cuarenta y seis . setenta y cinco (x- cuatro .8)^ dos = cero
- 61.87 menos 8.5 multiplicar por x al cuadrado menos 18x más 4(x menos 1.6) al cubo menos 46.75(x menos 4.8) al cuadrado es igual a 0
- sesenta y uno . ochenta y siete menos ocho . cinco multiplicar por x en el grado dos menos uno ocho x más cuatro (x menos 1. seis) en el grado tres menos cuarenta y seis . setenta y cinco (x menos cuatro .8) en el grado dos es igual a cero
- 61.87-8.5*x2-18x+4(x-1.6)3-46.75(x-4.8)2=0
- 61.87-8.5*x2-18x+4x-1.63-46.75x-4.82=0
- 61.87-8.5*x²-18x+4(x-1.6)³-46.75(x-4.8)²=0
- 61.87-8.5*x en el grado 2-18x+4(x-1.6) en el grado 3-46.75(x-4.8) en el grado 2=0
- 61.87-8.5x^2-18x+4(x-1.6)^3-46.75(x-4.8)^2=0
- 61.87-8.5x2-18x+4(x-1.6)3-46.75(x-4.8)2=0
- 61.87-8.5x2-18x+4x-1.63-46.75x-4.82=0
- 61.87-8.5x^2-18x+4x-1.6^3-46.75x-4.8^2=0
- 61.87-8.5*x^2-18x+4(x-1.6)^3-46.75(x-4.8)^2=O
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Expresiones semejantes
- 61.87+8.5*x^2-18x+4(x-1.6)^3-46.75(x-4.8)^2=0
- 61.87-8.5*x^2-18x+4(x+1.6)^3-46.75(x-4.8)^2=0
- 61.87-8.5*x^2-18x+4(x-1.6)^3-46.75(x+4.8)^2=0
- 61.87-8.5*x^2-18x+4(x-1.6)^3+46.75(x-4.8)^2=0
- 61.87-8.5*x^2+18x+4(x-1.6)^3-46.75(x-4.8)^2=0
- 61.87-8.5*x^2-18x-4(x-1.6)^3-46.75(x-4.8)^2=0
61.87-8.5*x^2-18x+4(x-1.6)^3-46.75(x-4.8)^2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 6187 17*x 3 187*(x - 24/5) ---- - ----- - 18*x + 4*(x - 8/5) - --------------- = 0 100 2 4
$$- \frac{187 \left(x - \frac{24}{5}\right)^{2}}{4} + \left(\left(- 18 x + \left(\frac{6187}{100} - \frac{17 x^{2}}{2}\right)\right) + 4 \left(x - \frac{8}{5}\right)^{3}\right) = 0$$
Suma y producto de raíces
[src]
suma
____________________________ / ____________________________ \ ____________________________ / ____________________________ \
/ _____________ | / _____________ | / _____________ | / _____________ |
/ 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 | ____________________________
3 / -------- + --------------- | \/ 3 *3 / -------- + --------------- ___ | 3 / -------- + --------------- |\/ 3 *3 / -------- + --------------- ___ | / _____________
1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 | 1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 | 1489 / 27218621 \/ 35727868731 73
---- - -------------------------------------- - --------------------------------- + I*|- --------------------------------------- + --------------------------------------| + ---- - -------------------------------------- - --------------------------------- + I*|--------------------------------------- - --------------------------------------| + ---- + 3 / -------- + --------------- + --------------------------------------
240 ____________________________ 2 | 2 ____________________________| 240 ____________________________ 2 | 2 ____________________________| 240 \/ 2764800 19200 ____________________________
/ _____________ | / _____________ | / _____________ | / _____________ | / _____________
/ 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731
4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- | 2304*3 / -------- + ---------------
\/ 2764800 19200 \ \/ 2764800 19200 / \/ 2764800 19200 \ \/ 2764800 19200 / \/ 2764800 19200
$$\left(\frac{73}{2304 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}} + \frac{1489}{240}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} + \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2}\right)\right)\right)$$
=
/ ____________________________ \ / ____________________________ \
| / _____________ | | / _____________ |
| ___ / 27218621 \/ 35727868731 | | ___ / 27218621 \/ 35727868731 |
|\/ 3 *3 / -------- + --------------- ___ | | \/ 3 *3 / -------- + --------------- ___ |
1489 | \/ 2764800 19200 73*\/ 3 | | \/ 2764800 19200 73*\/ 3 |
---- + I*|--------------------------------------- - --------------------------------------| + I*|- --------------------------------------- + --------------------------------------|
80 | 2 ____________________________| | 2 ____________________________|
| / _____________ | | / _____________ |
| / 27218621 \/ 35727868731 | | / 27218621 \/ 35727868731 |
| 4608*3 / -------- + --------------- | | 4608*3 / -------- + --------------- |
\ \/ 2764800 19200 / \ \/ 2764800 19200 /
$$\frac{1489}{80} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} + \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}\right) + i \left(- \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2}\right)$$
producto
/ ____________________________ / ____________________________ \\ / ____________________________ / ____________________________ \\ | / _____________ | / _____________ || | / _____________ | / _____________ || | / 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 || | / 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 || / ____________________________ \ | 3 / -------- + --------------- | \/ 3 *3 / -------- + --------------- ___ || | 3 / -------- + --------------- |\/ 3 *3 / -------- + --------------- ___ || | / _____________ | |1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 || |1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 || |1489 / 27218621 \/ 35727868731 73 | |---- - -------------------------------------- - --------------------------------- + I*|- --------------------------------------- + --------------------------------------||*|---- - -------------------------------------- - --------------------------------- + I*|--------------------------------------- - --------------------------------------||*|---- + 3 / -------- + --------------- + --------------------------------------| |240 ____________________________ 2 | 2 ____________________________|| |240 ____________________________ 2 | 2 ____________________________|| |240 \/ 2764800 19200 ____________________________| | / _____________ | / _____________ || | / _____________ | / _____________ || | / _____________ | | / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 || | / 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 || | / 27218621 \/ 35727868731 | | 4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- || | 4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- || | 2304*3 / -------- + --------------- | \ \/ 2764800 19200 \ \/ 2764800 19200 // \ \/ 2764800 19200 \ \/ 2764800 19200 // \ \/ 2764800 19200 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} + \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}\right)\right) \left(\frac{73}{2304 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}} + \frac{1489}{240}\right)$$
=
515817 ------ 2000
$$\frac{515817}{2000}$$
515817/2000
Respuesta rápida
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____________________________ / ____________________________ \
/ _____________ | / _____________ |
/ 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 |
3 / -------- + --------------- | \/ 3 *3 / -------- + --------------- ___ |
1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 |
x1 = ---- - -------------------------------------- - --------------------------------- + I*|- --------------------------------------- + --------------------------------------|
240 ____________________________ 2 | 2 ____________________________|
/ _____________ | / _____________ |
/ 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 |
4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- |
\/ 2764800 19200 \ \/ 2764800 19200 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} + \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}\right)$$
____________________________ / ____________________________ \
/ _____________ | / _____________ |
/ 27218621 \/ 35727868731 | ___ / 27218621 \/ 35727868731 |
3 / -------- + --------------- |\/ 3 *3 / -------- + --------------- ___ |
1489 73 \/ 2764800 19200 | \/ 2764800 19200 73*\/ 3 |
x2 = ---- - -------------------------------------- - --------------------------------- + I*|--------------------------------------- - --------------------------------------|
240 ____________________________ 2 | 2 ____________________________|
/ _____________ | / _____________ |
/ 27218621 \/ 35727868731 | / 27218621 \/ 35727868731 |
4608*3 / -------- + --------------- | 4608*3 / -------- + --------------- |
\/ 2764800 19200 \ \/ 2764800 19200 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2} - \frac{73}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{1489}{240} + i \left(- \frac{73 \sqrt{3}}{4608 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}}{2}\right)$$
____________________________
/ _____________
1489 / 27218621 \/ 35727868731 73
x3 = ---- + 3 / -------- + --------------- + --------------------------------------
240 \/ 2764800 19200 ____________________________
/ _____________
/ 27218621 \/ 35727868731
2304*3 / -------- + ---------------
\/ 2764800 19200
$$x_{3} = \frac{73}{2304 \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}}} + \sqrt[3]{\frac{\sqrt{35727868731}}{19200} + \frac{27218621}{2764800}} + \frac{1489}{240}$$
x3 = 73/(2304*(sqrt(35727868731)/19200 + 27218621/2764800)^(1/3)) + (sqrt(35727868731)/19200 + 27218621/2764800)^(1/3) + 1489/240
Respuesta numérica
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x1 = 4.84815371490857 - 2.3283602154035*i
x2 = 4.84815371490857 + 2.3283602154035*i
x3 = 8.91619257018287
x3 = 8.91619257018287