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Ecuación 6*x^2+x-7=0
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Ecuación (6*x+8)/2+5=5*x/3
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- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
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Expresiones idénticas
- dos /(dos -x)- uno / dos = cuatro / dos *x-x*x
- 2 dividir por (2 menos x) menos 1 dividir por 2 es igual a 4 dividir por 2 multiplicar por x menos x multiplicar por x
- dos dividir por (dos menos x) menos uno dividir por dos es igual a cuatro dividir por dos multiplicar por x menos x multiplicar por x
- 2/(2-x)-1/2=4/2x-xx
- 2/2-x-1/2=4/2x-xx
- 2 dividir por (2-x)-1 dividir por 2=4 dividir por 2*x-x*x
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Expresiones semejantes
- 2/(2-x)+1/2=4/2*x-x*x
- 2/(2+x)-1/2=4/2*x-x*x
- 2/(2-x)-1/2=4/2*x+x*x
2/(2-x)-1/2=4/2*x-x*x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 1 ----- - - = 2*x - x*x 2 - x 2
$$- \frac{1}{2} + \frac{2}{2 - x} = - x x + 2 x$$
Respuesta rápida
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_____________ / _____________ \
/ ____ | / ____ |
/ 29 \/ 78 | ___ / 29 \/ 78 |
3 / -- + ------ | \/ 3 *3 / -- + ------ ___ |
4 11 \/ 54 36 | \/ 54 36 11*\/ 3 |
x1 = - - --------------------- - ------------------ + I*|- ------------------------ + ---------------------|
3 _____________ 2 | 2 _____________|
/ ____ | / ____ |
/ 29 \/ 78 | / 29 \/ 78 |
36*3 / -- + ------ | 36*3 / -- + ------ |
\/ 54 36 \ \/ 54 36 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} + \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}\right)$$
_____________ / _____________ \
/ ____ | / ____ |
/ 29 \/ 78 | ___ / 29 \/ 78 |
3 / -- + ------ |\/ 3 *3 / -- + ------ ___ |
4 11 \/ 54 36 | \/ 54 36 11*\/ 3 |
x2 = - - --------------------- - ------------------ + I*|------------------------ - ---------------------|
3 _____________ 2 | 2 _____________|
/ ____ | / ____ |
/ 29 \/ 78 | / 29 \/ 78 |
36*3 / -- + ------ | 36*3 / -- + ------ |
\/ 54 36 \ \/ 54 36 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2}\right)$$
_____________
/ ____
4 / 29 \/ 78 11
x3 = - + 3 / -- + ------ + ---------------------
3 \/ 54 36 _____________
/ ____
/ 29 \/ 78
18*3 / -- + ------
\/ 54 36
$$x_{3} = \frac{11}{18 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}} + \frac{4}{3}$$
x3 = 11/(18*(sqrt(78)/36 + 29/54)^(1/3)) + (sqrt(78)/36 + 29/54)^(1/3) + 4/3
Suma y producto de raíces
[src]
suma
_____________ / _____________ \ _____________ / _____________ \
/ ____ | / ____ | / ____ | / ____ |
/ 29 \/ 78 | ___ / 29 \/ 78 | / 29 \/ 78 | ___ / 29 \/ 78 | _____________
3 / -- + ------ | \/ 3 *3 / -- + ------ ___ | 3 / -- + ------ |\/ 3 *3 / -- + ------ ___ | / ____
4 11 \/ 54 36 | \/ 54 36 11*\/ 3 | 4 11 \/ 54 36 | \/ 54 36 11*\/ 3 | 4 / 29 \/ 78 11
- - --------------------- - ------------------ + I*|- ------------------------ + ---------------------| + - - --------------------- - ------------------ + I*|------------------------ - ---------------------| + - + 3 / -- + ------ + ---------------------
3 _____________ 2 | 2 _____________| 3 _____________ 2 | 2 _____________| 3 \/ 54 36 _____________
/ ____ | / ____ | / ____ | / ____ | / ____
/ 29 \/ 78 | / 29 \/ 78 | / 29 \/ 78 | / 29 \/ 78 | / 29 \/ 78
36*3 / -- + ------ | 36*3 / -- + ------ | 36*3 / -- + ------ | 36*3 / -- + ------ | 18*3 / -- + ------
\/ 54 36 \ \/ 54 36 / \/ 54 36 \ \/ 54 36 / \/ 54 36
$$\left(\frac{11}{18 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}} + \frac{4}{3}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} + \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2}\right)\right)\right)$$
=
/ _____________ \ / _____________ \
| / ____ | | / ____ |
| ___ / 29 \/ 78 | | ___ / 29 \/ 78 |
|\/ 3 *3 / -- + ------ ___ | | \/ 3 *3 / -- + ------ ___ |
| \/ 54 36 11*\/ 3 | | \/ 54 36 11*\/ 3 |
4 + I*|------------------------ - ---------------------| + I*|- ------------------------ + ---------------------|
| 2 _____________| | 2 _____________|
| / ____ | | / ____ |
| / 29 \/ 78 | | / 29 \/ 78 |
| 36*3 / -- + ------ | | 36*3 / -- + ------ |
\ \/ 54 36 / \ \/ 54 36 /
$$4 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} + \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}\right) + i \left(- \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2}\right)$$
producto
/ _____________ / _____________ \\ / _____________ / _____________ \\ | / ____ | / ____ || | / ____ | / ____ || | / 29 \/ 78 | ___ / 29 \/ 78 || | / 29 \/ 78 | ___ / 29 \/ 78 || / _____________ \ | 3 / -- + ------ | \/ 3 *3 / -- + ------ ___ || | 3 / -- + ------ |\/ 3 *3 / -- + ------ ___ || | / ____ | |4 11 \/ 54 36 | \/ 54 36 11*\/ 3 || |4 11 \/ 54 36 | \/ 54 36 11*\/ 3 || |4 / 29 \/ 78 11 | |- - --------------------- - ------------------ + I*|- ------------------------ + ---------------------||*|- - --------------------- - ------------------ + I*|------------------------ - ---------------------||*|- + 3 / -- + ------ + ---------------------| |3 _____________ 2 | 2 _____________|| |3 _____________ 2 | 2 _____________|| |3 \/ 54 36 _____________| | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 29 \/ 78 | / 29 \/ 78 || | / 29 \/ 78 | / 29 \/ 78 || | / 29 \/ 78 | | 36*3 / -- + ------ | 36*3 / -- + ------ || | 36*3 / -- + ------ | 36*3 / -- + ------ || | 18*3 / -- + ------ | \ \/ 54 36 \ \/ 54 36 // \ \/ 54 36 \ \/ 54 36 // \ \/ 54 36 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} - \frac{11}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}{2} + \frac{11 \sqrt{3}}{36 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}}\right)\right) \left(\frac{11}{18 \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}}} + \sqrt[3]{\frac{\sqrt{78}}{36} + \frac{29}{54}} + \frac{4}{3}\right)$$
=
1
$$1$$
1
Respuesta numérica
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x1 = 0.54100602022967 - 0.223638949954783*i
x2 = 0.54100602022967 + 0.223638949954783*i
x3 = 2.91798795954066
x3 = 2.91798795954066