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- La ecuación:
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Ecuación x^3+3x^2-x-3=0
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Ecuación (x+9)^2=36*x
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Ecuación x^3-6x^2+11x-6=0
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Ecuación a+120=2000/5
- Expresar {x} en función de y en la ecuación:
- -6*x-12*y=9
- 9*x-1*y=17
- 10*x-2*y=11
- 12*x-3*y=-2
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Expresiones idénticas
- (cero . siete + cero . uno - dos . uno * cero . uno *x)*(uno + tres mil cuatrocientos treinta y ocho * cero . uno - dos *(cero . siete + cero . uno)*x+ dos . uno * cero . uno *x^ dos)= cero . siete * cero . uno *(seiscientos ochenta y siete . seis -(tres mil cuatrocientos treinta y ocho * cero . uno + uno)*x+(cero . siete + cero . uno)*x^ dos - cero . uno * cero . cinco *x^ tres)
- (0.7 más 0.01 menos 2.1 multiplicar por 0.01 multiplicar por x) multiplicar por (1 más 3438 multiplicar por 0.01 menos 2 multiplicar por (0.7 más 0.01) multiplicar por x más 2.1 multiplicar por 0.01 multiplicar por x al cuadrado ) es igual a 0.7 multiplicar por 0.01 multiplicar por (687.6 menos (3438 multiplicar por 0.01 más 1) multiplicar por x más (0.7 más 0.01) multiplicar por x al cuadrado menos 0.01 multiplicar por 0.5 multiplicar por x al cubo )
- (cero . siete más cero . uno menos dos . uno multiplicar por cero . uno multiplicar por x) multiplicar por (uno más tres mil cuatrocientos treinta y ocho multiplicar por cero . uno menos dos multiplicar por (cero . siete más cero . uno) multiplicar por x más dos . uno multiplicar por cero . uno multiplicar por x en el grado dos) es igual a cero . siete multiplicar por cero . uno multiplicar por (seiscientos ochenta y siete . seis menos (tres mil cuatrocientos treinta y ocho multiplicar por cero . uno más uno) multiplicar por x más (cero . siete más cero . uno) multiplicar por x en el grado dos menos cero . uno multiplicar por cero . cinco multiplicar por x en el grado tres)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x2-0.01*0.5*x3)
- 0.7+0.01-2.1*0.01*x*1+3438*0.01-2*0.7+0.01*x+2.1*0.01*x2=0.7*0.01*687.6-3438*0.01+1*x+0.7+0.01*x2-0.01*0.5*x3
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x²)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x²-0.01*0.5*x³)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x en el grado 2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x en el grado 2-0.01*0.5*x en el grado 3)
- (0.7+0.01-2.10.01x)(1+34380.01-2(0.7+0.01)x+2.10.01x^2)=0.70.01(687.6-(34380.01+1)x+(0.7+0.01)x^2-0.010.5x^3)
- (0.7+0.01-2.10.01x)(1+34380.01-2(0.7+0.01)x+2.10.01x2)=0.70.01(687.6-(34380.01+1)x+(0.7+0.01)x2-0.010.5x3)
- 0.7+0.01-2.10.01x1+34380.01-20.7+0.01x+2.10.01x2=0.70.01687.6-34380.01+1x+0.7+0.01x2-0.010.5x3
- 0.7+0.01-2.10.01x1+34380.01-20.7+0.01x+2.10.01x^2=0.70.01687.6-34380.01+1x+0.7+0.01x^2-0.010.5x^3
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=O.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
-
Expresiones semejantes
- (0.7+0.01+2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x-2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2+0.01*0.5*x^3)
- (0.7-0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1-3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6+(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01+2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7-0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01-1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7-0.01)*x^2-0.01*0.5*x^3)
- (0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x-(0.7+0.01)*x^2-0.01*0.5*x^3)
(0.7+0.01-2.1*0.01*x)*(1+3438*0.01-2*(0.7+0.01)*x+2.1*0.01*x^2)=0.7*0.01*(687.6-(3438*0.01+1)*x+(0.7+0.01)*x^2-0.01*0.5*x^3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 21 \ / 3438 21 2\ 7 /3438 /3438 \ 2 1 3\ |7/10 + 1/100 - ------*x|*|1 + ---- - 2*(7/10 + 1/100)*x + ------*x | = ------*|---- - |---- + 1|*x + (7/10 + 1/100)*x - -----*x | \ 10*100 / \ 100 10*100 / 10*100 \ 5 \100 / 100*2 /
$$\left(- \frac{21}{10 \cdot 100} x + \left(\frac{1}{100} + \frac{7}{10}\right)\right) \left(\frac{21}{10 \cdot 100} x^{2} + \left(- x 2 \left(\frac{1}{100} + \frac{7}{10}\right) + \left(1 + \frac{3438}{100}\right)\right)\right) = \frac{7}{10 \cdot 100} \left(- \frac{1}{2 \cdot 100} x^{3} + \left(x^{2} \left(\frac{1}{100} + \frac{7}{10}\right) + \left(- x \left(1 + \frac{3438}{100}\right) + \frac{3438}{5}\right)\right)\right)$$
Suma y producto de raíces
[src]
suma
______________________________________ / ______________________________________ \ ______________________________________ / ______________________________________\ ______________________________________
/ __________________ | / __________________ | / __________________ | / __________________ | / __________________
/ 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865
3 / ---------- + ----------------------- |\/ 3 *3 / ---------- + ----------------------- ___ | 3 / ---------- + ----------------------- | ___ \/ 3 *3 / ---------- + ----------------------- | 3 / ---------- + -----------------------
2840 4471960 \/ 170723 41209 | \/ 170723 41209 4471960*\/ 3 | 2840 4471960 \/ 170723 41209 | 4471960*\/ 3 \/ 170723 41209 | 2840 \/ 170723 41209 8943920
---- - ------------------------------------------------- + ------------------------------------------- + I*|------------------------------------------------- + -------------------------------------------------| + ---- - ------------------------------------------------- + ------------------------------------------- + I*|- ------------------------------------------------- - -------------------------------------------------| + ---- - ------------------------------------------- + -------------------------------------------------
87 ______________________________________ 6 | 6 ______________________________________| 87 ______________________________________ 6 | ______________________________________ 6 | 87 3 ______________________________________
/ __________________ | / __________________ | / __________________ | / __________________ | / __________________
/ 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865
17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + -----------------------
\/ 170723 41209 \ \/ 170723 41209 / \/ 170723 41209 \ \/ 170723 41209 / \/ 170723 41209
$$\left(- \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{3} + \frac{8943920}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{2840}{87}\right) + \left(\left(- \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} - \frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}\right)\right) + \left(- \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(\frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6}\right)\right)\right)$$
=
/ ______________________________________\ / ______________________________________ \
| / __________________ | | / __________________ |
| ___ / 2997671650 30*\/ 7198463224733865 | | ___ / 2997671650 30*\/ 7198463224733865 |
| ___ \/ 3 *3 / ---------- + ----------------------- | |\/ 3 *3 / ---------- + ----------------------- ___ |
2840 | 4471960*\/ 3 \/ 170723 41209 | | \/ 170723 41209 4471960*\/ 3 |
---- + I*|- ------------------------------------------------- - -------------------------------------------------| + I*|------------------------------------------------- + -------------------------------------------------|
29 | ______________________________________ 6 | | 6 ______________________________________|
| / __________________ | | / __________________ |
| / 2997671650 30*\/ 7198463224733865 | | / 2997671650 30*\/ 7198463224733865 |
| 17661*3 / ---------- + ----------------------- | | 17661*3 / ---------- + ----------------------- |
\ \/ 170723 41209 / \ \/ 170723 41209 /
$$\frac{2840}{29} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} - \frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}\right) + i \left(\frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6}\right)$$
producto
/ ______________________________________ / ______________________________________ \\ / ______________________________________ / ______________________________________\\ / ______________________________________ \ | / __________________ | / __________________ || | / __________________ | / __________________ || | / __________________ | | / 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 || | / 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 || | / 2997671650 30*\/ 7198463224733865 | | 3 / ---------- + ----------------------- |\/ 3 *3 / ---------- + ----------------------- ___ || | 3 / ---------- + ----------------------- | ___ \/ 3 *3 / ---------- + ----------------------- || | 3 / ---------- + ----------------------- | |2840 4471960 \/ 170723 41209 | \/ 170723 41209 4471960*\/ 3 || |2840 4471960 \/ 170723 41209 | 4471960*\/ 3 \/ 170723 41209 || |2840 \/ 170723 41209 8943920 | |---- - ------------------------------------------------- + ------------------------------------------- + I*|------------------------------------------------- + -------------------------------------------------||*|---- - ------------------------------------------------- + ------------------------------------------- + I*|- ------------------------------------------------- - -------------------------------------------------||*|---- - ------------------------------------------- + -------------------------------------------------| | 87 ______________________________________ 6 | 6 ______________________________________|| | 87 ______________________________________ 6 | ______________________________________ 6 || | 87 3 ______________________________________| | / __________________ | / __________________ || | / __________________ | / __________________ || | / __________________ | | / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 || | / 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 || | / 2997671650 30*\/ 7198463224733865 | | 17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- || | 17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- || | 17661*3 / ---------- + ----------------------- | \ \/ 170723 41209 \ \/ 170723 41209 // \ \/ 170723 41209 \ \/ 170723 41209 // \ \/ 170723 41209 /
$$\left(- \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(\frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6}\right)\right) \left(- \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} - \frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{3} + \frac{8943920}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{2840}{87}\right)$$
=
10153300 -------- 203
$$\frac{10153300}{203}$$
10153300/203
Respuesta rápida
[src]
______________________________________ / ______________________________________ \
/ __________________ | / __________________ |
/ 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 |
3 / ---------- + ----------------------- |\/ 3 *3 / ---------- + ----------------------- ___ |
2840 4471960 \/ 170723 41209 | \/ 170723 41209 4471960*\/ 3 |
x1 = ---- - ------------------------------------------------- + ------------------------------------------- + I*|------------------------------------------------- + -------------------------------------------------|
87 ______________________________________ 6 | 6 ______________________________________|
/ __________________ | / __________________ |
/ 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 |
17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- |
\/ 170723 41209 \ \/ 170723 41209 /
$$x_{1} = - \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(\frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6}\right)$$
______________________________________ / ______________________________________\
/ __________________ | / __________________ |
/ 2997671650 30*\/ 7198463224733865 | ___ / 2997671650 30*\/ 7198463224733865 |
3 / ---------- + ----------------------- | ___ \/ 3 *3 / ---------- + ----------------------- |
2840 4471960 \/ 170723 41209 | 4471960*\/ 3 \/ 170723 41209 |
x2 = ---- - ------------------------------------------------- + ------------------------------------------- + I*|- ------------------------------------------------- - -------------------------------------------------|
87 ______________________________________ 6 | ______________________________________ 6 |
/ __________________ | / __________________ |
/ 2997671650 30*\/ 7198463224733865 | / 2997671650 30*\/ 7198463224733865 |
17661*3 / ---------- + ----------------------- | 17661*3 / ---------- + ----------------------- |
\/ 170723 41209 \ \/ 170723 41209 /
$$x_{2} = - \frac{4471960}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} + \frac{2840}{87} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{6} - \frac{4471960 \sqrt{3}}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}\right)$$
______________________________________
/ __________________
/ 2997671650 30*\/ 7198463224733865
3 / ---------- + -----------------------
2840 \/ 170723 41209 8943920
x3 = ---- - ------------------------------------------- + -------------------------------------------------
87 3 ______________________________________
/ __________________
/ 2997671650 30*\/ 7198463224733865
17661*3 / ---------- + -----------------------
\/ 170723 41209
$$x_{3} = - \frac{\sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}}{3} + \frac{8943920}{17661 \sqrt[3]{\frac{2997671650}{170723} + \frac{30 \sqrt{7198463224733865}}{41209}}} + \frac{2840}{87}$$
x3 = -(2997671650/170723 + 30*sqrt(7198463224733865)/41209)^(1/3)/3 + 8943920/(17661*(2997671650/170723 + 30*sqrt(7198463224733865)/41209)^(1/3)) + 2840/87
Respuesta numérica
[src]
x1 = 33.9117231853917 + 22.6107468797091*i
x2 = 30.1075881119753
x3 = 33.9117231853917 - 22.6107468797091*i
x3 = 33.9117231853917 - 22.6107468797091*i