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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
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Ecuación -2*(-2-y)-y-2=0
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
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Expresiones idénticas
- x(x+ uno)(x- diez)=(uno -x)(x- tres)(x- cinco)
- x(x más 1)(x menos 10) es igual a (1 menos x)(x menos 3)(x menos 5)
- x(x más uno)(x menos diez) es igual a (uno menos x)(x menos tres)(x menos cinco)
- xx+1x-10=1-xx-3x-5
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Expresiones semejantes
- x(x-1)(x-10)=(1-x)(x-3)(x-5)
- x(x+1)(x-10)=(1+x)(x-3)(x-5)
- x(x+1)(x+10)=(1-x)(x-3)(x-5)
- x(x+1)(x-10)=(1-x)(x-3)(x+5)
- x(x+1)(x-10)=(1-x)(x+3)(x-5)
x(x+1)(x-10)=(1-x)(x-3)(x-5) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x*(x + 1)*(x - 10) = (1 - x)*(x - 3)*(x - 5)
$$x \left(x + 1\right) \left(x - 10\right) = \left(1 - x\right) \left(x - 3\right) \left(x - 5\right)$$
Suma y producto de raíces
[src]
suma
_________________ / _________________ \ _________________ / _________________ \
/ ________ | / ________ | / ________ | / ________ |
/ \/ 158010 | ___ / \/ 158010 | / \/ 158010 | ___ / \/ 158010 | _________________
3 / 21 + ---------- | \/ 3 *3 / 21 + ---------- ___ | 3 / 21 + ---------- |\/ 3 *3 / 21 + ---------- ___ | / ________
41 \/ 36 | \/ 36 41*\/ 3 | 41 \/ 36 | \/ 36 41*\/ 3 | / \/ 158010 41
3 - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------| + 3 - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------| + 3 + 3 / 21 + ---------- + ------------------------
_________________ 2 | 2 _________________| _________________ 2 | 2 _________________| \/ 36 _________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ \/ 158010 | / \/ 158010 | / \/ 158010 | / \/ 158010 | / \/ 158010
12*3 / 21 + ---------- | 12*3 / 21 + ---------- | 12*3 / 21 + ---------- | 12*3 / 21 + ---------- | 6*3 / 21 + ----------
\/ 36 \ \/ 36 / \/ 36 \ \/ 36 / \/ 36
$$\left(\frac{41}{6 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} + \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2}\right)\right)\right)$$
=
/ _________________ \ / _________________ \
| / ________ | | / ________ |
| ___ / \/ 158010 | | ___ / \/ 158010 |
|\/ 3 *3 / 21 + ---------- ___ | | \/ 3 *3 / 21 + ---------- ___ |
| \/ 36 41*\/ 3 | | \/ 36 41*\/ 3 |
9 + I*|---------------------------- - -------------------------| + I*|- ---------------------------- + -------------------------|
| 2 _________________| | 2 _________________|
| / ________ | | / ________ |
| / \/ 158010 | | / \/ 158010 |
| 12*3 / 21 + ---------- | | 12*3 / 21 + ---------- |
\ \/ 36 / \ \/ 36 /
$$9 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} + \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}\right) + i \left(- \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2}\right)$$
producto
/ _________________ / _________________ \\ / _________________ / _________________ \\ | / ________ | / ________ || | / ________ | / ________ || | / \/ 158010 | ___ / \/ 158010 || | / \/ 158010 | ___ / \/ 158010 || / _________________ \ | 3 / 21 + ---------- | \/ 3 *3 / 21 + ---------- ___ || | 3 / 21 + ---------- |\/ 3 *3 / 21 + ---------- ___ || | / ________ | | 41 \/ 36 | \/ 36 41*\/ 3 || | 41 \/ 36 | \/ 36 41*\/ 3 || | / \/ 158010 41 | |3 - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------||*|3 - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------||*|3 + 3 / 21 + ---------- + ------------------------| | _________________ 2 | 2 _________________|| | _________________ 2 | 2 _________________|| | \/ 36 _________________| | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / \/ 158010 | / \/ 158010 || | / \/ 158010 | / \/ 158010 || | / \/ 158010 | | 12*3 / 21 + ---------- | 12*3 / 21 + ---------- || | 12*3 / 21 + ---------- | 12*3 / 21 + ---------- || | 6*3 / 21 + ---------- | \ \/ 36 \ \/ 36 // \ \/ 36 \ \/ 36 // \ \/ 36 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} + \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}\right)\right) \left(\frac{41}{6 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}\right)$$
=
15/2
$$\frac{15}{2}$$
15/2
Respuesta rápida
[src]
_________________ / _________________ \
/ ________ | / ________ |
/ \/ 158010 | ___ / \/ 158010 |
3 / 21 + ---------- | \/ 3 *3 / 21 + ---------- ___ |
41 \/ 36 | \/ 36 41*\/ 3 |
x1 = 3 - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------|
_________________ 2 | 2 _________________|
/ ________ | / ________ |
/ \/ 158010 | / \/ 158010 |
12*3 / 21 + ---------- | 12*3 / 21 + ---------- |
\/ 36 \ \/ 36 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} + \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}\right)$$
_________________ / _________________ \
/ ________ | / ________ |
/ \/ 158010 | ___ / \/ 158010 |
3 / 21 + ---------- |\/ 3 *3 / 21 + ---------- ___ |
41 \/ 36 | \/ 36 41*\/ 3 |
x2 = 3 - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------|
_________________ 2 | 2 _________________|
/ ________ | / ________ |
/ \/ 158010 | / \/ 158010 |
12*3 / 21 + ---------- | 12*3 / 21 + ---------- |
\/ 36 \ \/ 36 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2} - \frac{41}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + i \left(- \frac{41 \sqrt{3}}{12 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}}{2}\right)$$
_________________
/ ________
/ \/ 158010 41
x3 = 3 + 3 / 21 + ---------- + ------------------------
\/ 36 _________________
/ ________
/ \/ 158010
6*3 / 21 + ----------
\/ 36
$$x_{3} = \frac{41}{6 \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}} + 3 + \sqrt[3]{\frac{\sqrt{158010}}{36} + 21}$$
x3 = 41/(6*(sqrt(158010)/36 + 21)^(1/3)) + 3 + (sqrt(158010)/36 + 21)^(1/3)
Respuesta numérica
[src]
x1 = 0.336193696911665 + 0.887463836513598*i
x2 = 8.32761260617667
x3 = 0.336193696911665 - 0.887463836513598*i
x3 = 0.336193696911665 - 0.887463836513598*i