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- La ecuación:
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Ecuación 1/(x-3)^2-3/(x-3)-4=0
-
Ecuación 9*(x-5)=-x
-
Ecuación 13x+10=6x-4
- Ecuación x-y=1
- Expresar {x} en función de y en la ecuación:
- 7*x-6*y=-2
- 13*x-15*y=-6
- 4*x-7*y=4
- -4*x+6*y=-7
-
Expresiones idénticas
- sqrt((x+ cinco)/x)+ cuatro *sqrt((x/ cinco +x))= cuatro
- raíz cuadrada de ((x más 5) dividir por x) más 4 multiplicar por raíz cuadrada de ((x dividir por 5 más x)) es igual a 4
- raíz cuadrada de ((x más cinco) dividir por x) más cuatro multiplicar por raíz cuadrada de ((x dividir por cinco más x)) es igual a cuatro
- √((x+5)/x)+4*√((x/5+x))=4
- sqrt((x+5)/x)+4sqrt((x/5+x))=4
- sqrtx+5/x+4sqrtx/5+x=4
- sqrt((x+5) dividir por x)+4*sqrt((x dividir por 5+x))=4
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Expresiones semejantes
- sqrt((x-5)/x)+4*sqrt((x/5+x))=4
- sqrt((x+5)/x)-4*sqrt((x/5+x))=4
- sqrt((x+5)/x)+4*sqrt((x/5-x))=4
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+4)=x-3
- sqrt(5+|x-2|)=1-x
- sqrt(6+5*x)=x
- sqrt(x-2)=6
- sqrt(3+2*x)=x
- Raíz cuadrada sqrt
- sqrt(x+4)=x-3
- sqrt(5+|x-2|)=1-x
- sqrt(6+5*x)=x
- sqrt(x-2)=6
- sqrt(3+2*x)=x
sqrt((x+5)/x)+4*sqrt((x/5+x))=4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_______ _______ / x + 5 / x / ----- + 4* / - + x = 4 \/ x \/ 5
$$\sqrt{\frac{x + 5}{x}} + 4 \sqrt{\frac{x}{5} + x} = 4$$
Suma y producto de raíces
[src]
suma
____________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________
/ _________________________________ / _________________________________
/ / _______ / / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 14125 / 2225 / 133301796875 15625*\/ 33554 12644375 14125
I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------- I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------
____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________ ____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________
/ _________________________________ / / _______ / _________________________________ / _________________________________ / / _______ / _________________________________
/ / _______ / / 133301796875 15625*\/ 33554 / / _______ / / _______ / / 133301796875 15625*\/ 33554 / / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375 / 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375
/ ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------
/ 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________ / 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________
/ / _______ / / / _______ / / _______ / / / _______
/ / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554 / / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554
/ 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + --------------- / 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + ---------------
85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984 85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984
--- - -------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --- - -------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
192 2 2 192 2 2
$$\left(- \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} - \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}\right) + \left(- \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} + \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}\right)$$
=
____________________________________________________________________________________________________
/ _________________________________
/ / _______
85 / 2225 / 133301796875 15625*\/ 33554 12644375
-- - / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------
96 / 3072 \/ 6262062317568 127401984 _________________________________
/ / _______
/ / 133301796875 15625*\/ 33554
/ 169869312*3 / ------------- + ---------------
\/ \/ 6262062317568 127401984
$$\frac{85}{96} - \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}$$
producto
/ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________\ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________________\ | / _________________________________ | | / _________________________________ | | / / _______ | | / / _______ | | / 2225 / 133301796875 15625*\/ 33554 12644375 14125 | | / 2225 / 133301796875 15625*\/ 33554 12644375 14125 | | I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------- | | I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------- | | ____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________ | | ____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________ | | / _________________________________ / / _______ / _________________________________ | | / _________________________________ / / _______ / _________________________________ | | / / _______ / / 133301796875 15625*\/ 33554 / / _______ | | / / _______ / / 133301796875 15625*\/ 33554 / / _______ | | / 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375 | | / 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375 | | / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ | | / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ | | / 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________ | | / 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554 | | / / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554 | | / 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + --------------- | | / 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + --------------- | | 85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984 | | 85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984 | |--- - -------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|--- - -------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \192 2 2 / \192 2 2 /
$$\left(- \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} - \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} + \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}\right)$$
=
___________________________
_______ 6 / _______ _______
275 505775 213282875 3625808875 200*\/ 33554 67325*\/ 8531315 + 49152*\/ 33554 8598175 3400*\/ 33554
----- - ------------------------------------ + ------------------------------------ - ----------------------------------------------------------------------------------------------------------------------- + -------------------------------- + ---------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------
18432 ___________________________ 2/3 ______________________________________________________________________________ 2/3 ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________
3 / _______ / _______\ ___________________________ / 2/3 ___________________________ / _______\ / 2/3 ___________________________ ___________________________ / 2/3 ___________________________ ___________________________ / 2/3 ___________________________
18432*\/ 8531315 + 49152*\/ 33554 18432*\8531315 + 49152*\/ 33554 / / _______ / / _______\ 3 / _______ 3*\8531315 + 49152*\/ 33554 / / / _______\ 3 / _______ 6 / _______ / / _______\ 3 / _______ / _______ / / _______\ 3 / _______
18432*\/ 8531315 + 49152*\/ 33554 *\/ -20231 + \8531315 + 49152*\/ 33554 / + 267*\/ 8531315 + 49152*\/ 33554 18432*\/ -20231 + \8531315 + 49152*\/ 33554 / + 267*\/ 8531315 + 49152*\/ 33554 18432*\/ 8531315 + 49152*\/ 33554 *\/ -20231 + \8531315 + 49152*\/ 33554 / + 267*\/ 8531315 + 49152*\/ 33554 3*\/ 8531315 + 49152*\/ 33554 *\/ -20231 + \8531315 + 49152*\/ 33554 / + 267*\/ 8531315 + 49152*\/ 33554
$$- \frac{3400 \sqrt{33554}}{3 \sqrt{8531315 + 49152 \sqrt{33554}} \sqrt{-20231 + \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}} + 267 \sqrt[3]{8531315 + 49152 \sqrt{33554}}}} - \frac{3625808875}{18432 \sqrt{8531315 + 49152 \sqrt{33554}} \sqrt{-20231 + \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}} + 267 \sqrt[3]{8531315 + 49152 \sqrt{33554}}}} - \frac{505775}{18432 \sqrt[3]{8531315 + 49152 \sqrt{33554}}} + \frac{275}{18432} + \frac{8598175}{18432 \sqrt[6]{8531315 + 49152 \sqrt{33554}} \sqrt{-20231 + \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}} + 267 \sqrt[3]{8531315 + 49152 \sqrt{33554}}}} + \frac{213282875}{18432 \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}}} + \frac{67325 \sqrt[6]{8531315 + 49152 \sqrt{33554}}}{18432 \sqrt{-20231 + \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}} + 267 \sqrt[3]{8531315 + 49152 \sqrt{33554}}}} + \frac{200 \sqrt{33554}}{3 \left(8531315 + 49152 \sqrt{33554}\right)^{\frac{2}{3}}}$$
275/18432 - 505775/(18432*(8531315 + 49152*sqrt(33554))^(1/3)) + 213282875/(18432*(8531315 + 49152*sqrt(33554))^(2/3)) - 3625808875/(18432*sqrt(8531315 + 49152*sqrt(33554))*sqrt(-20231 + (8531315 + 49152*sqrt(33554))^(2/3) + 267*(8531315 + 49152*sqrt(33554))^(1/3))) + 200*sqrt(33554)/(3*(8531315 + 49152*sqrt(33554))^(2/3)) + 67325*(8531315 + 49152*sqrt(33554))^(1/6)/(18432*sqrt(-20231 + (8531315 + 49152*sqrt(33554))^(2/3) + 267*(8531315 + 49152*sqrt(33554))^(1/3))) + 8598175/(18432*(8531315 + 49152*sqrt(33554))^(1/6)*sqrt(-20231 + (8531315 + 49152*sqrt(33554))^(2/3) + 267*(8531315 + 49152*sqrt(33554))^(1/3))) - 3400*sqrt(33554)/(3*sqrt(8531315 + 49152*sqrt(33554))*sqrt(-20231 + (8531315 + 49152*sqrt(33554))^(2/3) + 267*(8531315 + 49152*sqrt(33554))^(1/3)))
Respuesta rápida
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____________________________________________________________________________________________________________________________________________________________________________________________________________________________
/ _________________________________
/ / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 14125
I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------
____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________
/ _________________________________ / / _______ / _________________________________
/ / _______ / / 133301796875 15625*\/ 33554 / / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375
/ ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------
/ 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________
/ / _______ / / / _______
/ / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554
/ 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + ---------------
85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984
x1 = --- - -------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
192 2 2
$$x_{1} = - \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} - \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}$$
____________________________________________________________________________________________________________________________________________________________________________________________________________________________
/ _________________________________
/ / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 14125
I* / - ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------
____________________________________________________________________________________________________ / 1536 \/ 6262062317568 127401984 _________________________________ ____________________________________________________________________________________________________
/ _________________________________ / / _______ / _________________________________
/ / _______ / / 133301796875 15625*\/ 33554 / / _______
/ 2225 / 133301796875 15625*\/ 33554 12644375 / 169869312*3 / ------------- + --------------- / 2225 / 133301796875 15625*\/ 33554 12644375
/ ---- + 2*3 / ------------- + --------------- - ------------------------------------------------ / \/ 6262062317568 127401984 6912* / ---- + 2*3 / ------------- + --------------- - ------------------------------------------------
/ 3072 \/ 6262062317568 127401984 _________________________________ / / 3072 \/ 6262062317568 127401984 _________________________________
/ / _______ / / / _______
/ / 133301796875 15625*\/ 33554 / / / 133301796875 15625*\/ 33554
/ 169869312*3 / ------------- + --------------- / / 169869312*3 / ------------- + ---------------
85 \/ \/ 6262062317568 127401984 \/ \/ \/ 6262062317568 127401984
x2 = --- - -------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
192 2 2
$$x_{2} = - \frac{\sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}{2} + \frac{85}{192} + \frac{i \sqrt{- \frac{2225}{1536} - \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{14125}{6912 \sqrt{- \frac{12644375}{169869312 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}}} + 2 \sqrt[3]{\frac{133301796875}{6262062317568} + \frac{15625 \sqrt{33554}}{127401984}} + \frac{2225}{3072}}}}}{2}$$
x2 = -sqrt(-12644375/(169869312*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3)) + 2*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3) + 2225/3072)/2 + 85/192 + i*sqrt(-2225/1536 - 12644375/(169869312*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3)) + 2*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3) + 14125/(6912*sqrt(-12644375/(169869312*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3)) + 2*(133301796875/6262062317568 + 15625*sqrt(33554)/127401984)^(1/3) + 2225/3072)))/2
Respuesta numérica
[src]
x1 = -0.109058362443569 - 0.473486119482776*i
x2 = -0.109058362443569 + 0.473486119482776*i
x3 = -0.109058362443569 + 0.473486119482776*i
x3 = -0.109058362443569 + 0.473486119482776*i