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Ecuación x^2-11*x+30=0
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Ecuación -33-y=-19
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Ecuación 11/(x-9)=-10
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
- x- tres / dos *(x- uno)^(dos / tres)= cero
- x menos 3 dividir por 2 multiplicar por (x menos 1) en el grado (2 dividir por 3) es igual a 0
- x menos tres dividir por dos multiplicar por (x menos uno) en el grado (dos dividir por tres) es igual a cero
- x-3/2*(x-1)(2/3)=0
- x-3/2*x-12/3=0
- x-3/2(x-1)^(2/3)=0
- x-3/2(x-1)(2/3)=0
- x-3/2x-12/3=0
- x-3/2x-1^2/3=0
- x-3/2*(x-1)^(2/3)=O
- x-3 dividir por 2*(x-1)^(2 dividir por 3)=0
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Expresiones semejantes
- x+3/2*(x-1)^(2/3)=0
- x-3/2*(x+1)^(2/3)=0
x-3/2*(x-1)^(2/3)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2/3
3*(x - 1)
x - ------------ = 0
2
$$x - \frac{3 \left(x - 1\right)^{\frac{2}{3}}}{2} = 0$$
Suma y producto de raíces
[src]
suma
________________ / ________________ \ ________________ / ________________\
/ ___ | / ___ | / ___ | / ___ |
/ 351 27*\/ 2 | ___ / 351 27*\/ 2 | / 351 27*\/ 2 | ___ / 351 27*\/ 2 |
3 / --- + -------- |\/ 3 *3 / --- + -------- ___ | 3 / --- + -------- | ___ \/ 3 *3 / --- + -------- |
9 \/ 512 32 63 | \/ 512 32 63*\/ 3 | 9 \/ 512 32 63 | 63*\/ 3 \/ 512 32 |
- + --------------------- - ------------------------- + I*|--------------------------- + -------------------------| + - + --------------------- - ------------------------- + I*|- ------------------------- - ---------------------------|
8 2 ________________ | 2 ________________| 8 2 ________________ | ________________ 2 |
/ ___ | / ___ | / ___ | / ___ |
/ 351 27*\/ 2 | / 351 27*\/ 2 | / 351 27*\/ 2 | / 351 27*\/ 2 |
128*3 / --- + -------- | 128*3 / --- + -------- | 128*3 / --- + -------- | 128*3 / --- + -------- |
\/ 512 32 \ \/ 512 32 / \/ 512 32 \ \/ 512 32 /
$$\left(- \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} - \frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}\right)\right) + \left(- \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(\frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2}\right)\right)$$
=
/ ________________ \ / ________________\
| / ___ | | / ___ |
________________ | ___ / 351 27*\/ 2 | | ___ / 351 27*\/ 2 |
/ ___ |\/ 3 *3 / --- + -------- ___ | | ___ \/ 3 *3 / --- + -------- |
9 / 351 27*\/ 2 63 | \/ 512 32 63*\/ 3 | | 63*\/ 3 \/ 512 32 |
- + 3 / --- + -------- - ------------------------ + I*|--------------------------- + -------------------------| + I*|- ------------------------- - ---------------------------|
4 \/ 512 32 ________________ | 2 ________________| | ________________ 2 |
/ ___ | / ___ | | / ___ |
/ 351 27*\/ 2 | / 351 27*\/ 2 | | / 351 27*\/ 2 |
64*3 / --- + -------- | 128*3 / --- + -------- | | 128*3 / --- + -------- |
\/ 512 32 \ \/ 512 32 / \ \/ 512 32 /
$$- \frac{63}{64 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}} + \frac{9}{4} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} - \frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}\right) + i \left(\frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2}\right)$$
producto
/ ________________ / ________________ \\ / ________________ / ________________\\ | / ___ | / ___ || | / ___ | / ___ || | / 351 27*\/ 2 | ___ / 351 27*\/ 2 || | / 351 27*\/ 2 | ___ / 351 27*\/ 2 || | 3 / --- + -------- |\/ 3 *3 / --- + -------- ___ || | 3 / --- + -------- | ___ \/ 3 *3 / --- + -------- || |9 \/ 512 32 63 | \/ 512 32 63*\/ 3 || |9 \/ 512 32 63 | 63*\/ 3 \/ 512 32 || |- + --------------------- - ------------------------- + I*|--------------------------- + -------------------------||*|- + --------------------- - ------------------------- + I*|- ------------------------- - ---------------------------|| |8 2 ________________ | 2 ________________|| |8 2 ________________ | ________________ 2 || | / ___ | / ___ || | / ___ | / ___ || | / 351 27*\/ 2 | / 351 27*\/ 2 || | / 351 27*\/ 2 | / 351 27*\/ 2 || | 128*3 / --- + -------- | 128*3 / --- + -------- || | 128*3 / --- + -------- | 128*3 / --- + -------- || \ \/ 512 32 \ \/ 512 32 // \ \/ 512 32 \ \/ 512 32 //
$$\left(- \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(\frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2}\right)\right) \left(- \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} - \frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}\right)\right)$$
=
/ _______________ 2/3 _______________\
| 3 / ___ / ___\ ___ ___ 3 / ___ |
9*\11 - \/ 13 + 16*\/ 2 + 2*\13 + 16*\/ 2 / + 6*\/ 2 + 2*\/ 2 *\/ 13 + 16*\/ 2 /
-----------------------------------------------------------------------------------------
2/3
/ ___\
8*\13 + 16*\/ 2 /
$$\frac{9 \left(- \sqrt[3]{13 + 16 \sqrt{2}} + 6 \sqrt{2} + 2 \sqrt{2} \sqrt[3]{13 + 16 \sqrt{2}} + 11 + 2 \left(13 + 16 \sqrt{2}\right)^{\frac{2}{3}}\right)}{8 \left(13 + 16 \sqrt{2}\right)^{\frac{2}{3}}}$$
9*(11 - (13 + 16*sqrt(2))^(1/3) + 2*(13 + 16*sqrt(2))^(2/3) + 6*sqrt(2) + 2*sqrt(2)*(13 + 16*sqrt(2))^(1/3))/(8*(13 + 16*sqrt(2))^(2/3))
Respuesta rápida
[src]
________________ / ________________ \
/ ___ | / ___ |
/ 351 27*\/ 2 | ___ / 351 27*\/ 2 |
3 / --- + -------- |\/ 3 *3 / --- + -------- ___ |
9 \/ 512 32 63 | \/ 512 32 63*\/ 3 |
x1 = - + --------------------- - ------------------------- + I*|--------------------------- + -------------------------|
8 2 ________________ | 2 ________________|
/ ___ | / ___ |
/ 351 27*\/ 2 | / 351 27*\/ 2 |
128*3 / --- + -------- | 128*3 / --- + -------- |
\/ 512 32 \ \/ 512 32 /
$$x_{1} = - \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(\frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2}\right)$$
________________ / ________________\
/ ___ | / ___ |
/ 351 27*\/ 2 | ___ / 351 27*\/ 2 |
3 / --- + -------- | ___ \/ 3 *3 / --- + -------- |
9 \/ 512 32 63 | 63*\/ 3 \/ 512 32 |
x2 = - + --------------------- - ------------------------- + I*|- ------------------------- - ---------------------------|
8 2 ________________ | ________________ 2 |
/ ___ | / ___ |
/ 351 27*\/ 2 | / 351 27*\/ 2 |
128*3 / --- + -------- | 128*3 / --- + -------- |
\/ 512 32 \ \/ 512 32 /
$$x_{2} = - \frac{63}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}} + \frac{\sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} + \frac{9}{8} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}{2} - \frac{63 \sqrt{3}}{128 \sqrt[3]{\frac{351}{512} + \frac{27 \sqrt{2}}{32}}}\right)$$
x2 = -63/(128*(351/512 + 27*sqrt(2)/32)^(1/3)) + (351/512 + 27*sqrt(2)/32)^(1/3)/2 + 9/8 + i*(-sqrt(3)*(351/512 + 27*sqrt(2)/32)^(1/3)/2 - 63*sqrt(3)/(128*(351/512 + 27*sqrt(2)/32)^(1/3)))
Respuesta numérica
[src]
x1 = 1.34309214780778 + 1.75949355065775*i
x2 = 1.34309214780778 - 1.75949355065775*i
x2 = 1.34309214780778 - 1.75949355065775*i