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- La ecuación:
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Ecuación -x+7=0
-
Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
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Ecuación z^3=8
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- sqrt(ocho *x^ dos - cuarenta y dos *x^ tres +x)-x*sqrt(cuatro -x)- dos *sqrt(cuatro -x)= cero
- raíz cuadrada de (8 multiplicar por x al cuadrado menos 42 multiplicar por x al cubo más x) menos x multiplicar por raíz cuadrada de (4 menos x) menos 2 multiplicar por raíz cuadrada de (4 menos x) es igual a 0
- raíz cuadrada de (ocho multiplicar por x en el grado dos menos cuarenta y dos multiplicar por x en el grado tres más x) menos x multiplicar por raíz cuadrada de (cuatro menos x) menos dos multiplicar por raíz cuadrada de (cuatro menos x) es igual a cero
- √(8*x^2-42*x^3+x)-x*√(4-x)-2*√(4-x)=0
- sqrt(8*x2-42*x3+x)-x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt8*x2-42*x3+x-x*sqrt4-x-2*sqrt4-x=0
- sqrt(8*x²-42*x³+x)-x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt(8*x en el grado 2-42*x en el grado 3+x)-x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt(8x^2-42x^3+x)-xsqrt(4-x)-2sqrt(4-x)=0
- sqrt(8x2-42x3+x)-xsqrt(4-x)-2sqrt(4-x)=0
- sqrt8x2-42x3+x-xsqrt4-x-2sqrt4-x=0
- sqrt8x^2-42x^3+x-xsqrt4-x-2sqrt4-x=0
- sqrt(8*x^2-42*x^3+x)-x*sqrt(4-x)-2*sqrt(4-x)=O
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Expresiones semejantes
- sqrt(8*x^2-42*x^3+x)-x*sqrt(4+x)-2*sqrt(4-x)=0
- sqrt(8*x^2-42*x^3+x)-x*sqrt(4-x)+2*sqrt(4-x)=0
- sqrt(8*x^2+42*x^3+x)-x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt(8*x^2-42*x^3-x)-x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt(8*x^2-42*x^3+x)+x*sqrt(4-x)-2*sqrt(4-x)=0
- sqrt(8*x^2-42*x^3+x)-x*sqrt(4-x)-2*sqrt(4+x)=0
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(4*sin(x)^2+1)+sqrt(4*cos(x)^2+3)=4
- sqrt(5x)=2x(1/2)
- sqrt5(x−23)=−3
- sqrt(3x-5b)=5b-2x
- sqrt(3)*x/sqrt(x^2-8*x-64)=383/1000
- Raíz cuadrada sqrt
- sqrt(4*sin(x)^2+1)+sqrt(4*cos(x)^2+3)=4
- sqrt(5x)=2x(1/2)
- sqrt5(x−23)=−3
- sqrt(3x-5b)=5b-2x
- sqrt(3)*x/sqrt(x^2-8*x-64)=383/1000
- Raíz cuadrada sqrt
- sqrt(4*sin(x)^2+1)+sqrt(4*cos(x)^2+3)=4
- sqrt(5x)=2x(1/2)
- sqrt5(x−23)=−3
- sqrt(3x-5b)=5b-2x
- sqrt(3)*x/sqrt(x^2-8*x-64)=383/1000
sqrt(8*x^2-42*x^3+x)-x*sqrt(4-x)-2*sqrt(4-x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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__________________ / 2 3 _______ _______ \/ 8*x - 42*x + x - x*\/ 4 - x - 2*\/ 4 - x = 0
$$- 2 \sqrt{4 - x} + \left(- x \sqrt{4 - x} + \sqrt{x + \left(- 42 x^{3} + 8 x^{2}\right)}\right) = 0$$
Suma y producto de raíces
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suma
________________________ / ________________________ \ ________________________ / ________________________\ ________________________
/ _________ | / _________ | / _________ | / _________ | / _________
/ 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961
3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ | 3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- | 3 / ------ + -------------
8 1289 \/ 68921 1681 | \/ 68921 1681 1289*\/ 3 | 8 1289 \/ 68921 1681 | 1289*\/ 3 \/ 68921 1681 | 8 \/ 68921 1681 1289
--- - ----------------------------------- + ----------------------------- + I*|----------------------------------- + -----------------------------------| + --- - ----------------------------------- + ----------------------------- + I*|- ----------------------------------- - -----------------------------------| + --- - ----------------------------- + ----------------------------------
123 ________________________ 6 | 6 ________________________| 123 ________________________ 6 | ________________________ 6 | 123 3 ________________________
/ _________ | / _________ | / _________ | / _________ | / _________
/ 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961
10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- | 5043*3 / ------ + -------------
\/ 68921 1681 \ \/ 68921 1681 / \/ 68921 1681 \ \/ 68921 1681 / \/ 68921 1681
$$\left(- \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{3} + \frac{8}{123} + \frac{1289}{5043 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right) + \left(\left(- \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} - \frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right)\right) + \left(- \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(\frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6}\right)\right)\right)$$
=
/ ________________________\ / ________________________ \
| / _________ | | / _________ |
| ___ / 378820 3*\/ 9626961 | | ___ / 378820 3*\/ 9626961 |
| ___ \/ 3 *3 / ------ + ------------- | |\/ 3 *3 / ------ + ------------- ___ |
8 | 1289*\/ 3 \/ 68921 1681 | | \/ 68921 1681 1289*\/ 3 |
-- + I*|- ----------------------------------- - -----------------------------------| + I*|----------------------------------- + -----------------------------------|
41 | ________________________ 6 | | 6 ________________________|
| / _________ | | / _________ |
| / 378820 3*\/ 9626961 | | / 378820 3*\/ 9626961 |
| 10086*3 / ------ + ------------- | | 10086*3 / ------ + ------------- |
\ \/ 68921 1681 / \ \/ 68921 1681 /
$$\frac{8}{41} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} - \frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right) + i \left(\frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6}\right)$$
producto
/ ________________________ / ________________________ \\ / ________________________ / ________________________\\ / ________________________ \ | / _________ | / _________ || | / _________ | / _________ || | / _________ | | / 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 || | / 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 || | / 378820 3*\/ 9626961 | | 3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ || | 3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- || | 3 / ------ + ------------- | | 8 1289 \/ 68921 1681 | \/ 68921 1681 1289*\/ 3 || | 8 1289 \/ 68921 1681 | 1289*\/ 3 \/ 68921 1681 || | 8 \/ 68921 1681 1289 | |--- - ----------------------------------- + ----------------------------- + I*|----------------------------------- + -----------------------------------||*|--- - ----------------------------------- + ----------------------------- + I*|- ----------------------------------- - -----------------------------------||*|--- - ----------------------------- + ----------------------------------| |123 ________________________ 6 | 6 ________________________|| |123 ________________________ 6 | ________________________ 6 || |123 3 ________________________| | / _________ | / _________ || | / _________ | / _________ || | / _________ | | / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 || | / 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 || | / 378820 3*\/ 9626961 | | 10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- || | 10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- || | 5043*3 / ------ + ------------- | \ \/ 68921 1681 \ \/ 68921 1681 // \ \/ 68921 1681 \ \/ 68921 1681 // \ \/ 68921 1681 /
$$\left(- \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(\frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6}\right)\right) \left(- \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} - \frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{3} + \frac{8}{123} + \frac{1289}{5043 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right)$$
=
-16 ---- 41
$$- \frac{16}{41}$$
-16/41
Respuesta rápida
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________________________ / ________________________ \
/ _________ | / _________ |
/ 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 |
3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ |
8 1289 \/ 68921 1681 | \/ 68921 1681 1289*\/ 3 |
x1 = --- - ----------------------------------- + ----------------------------- + I*|----------------------------------- + -----------------------------------|
123 ________________________ 6 | 6 ________________________|
/ _________ | / _________ |
/ 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 |
10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- |
\/ 68921 1681 \ \/ 68921 1681 /
$$x_{1} = - \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(\frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6}\right)$$
________________________ / ________________________\
/ _________ | / _________ |
/ 378820 3*\/ 9626961 | ___ / 378820 3*\/ 9626961 |
3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- |
8 1289 \/ 68921 1681 | 1289*\/ 3 \/ 68921 1681 |
x2 = --- - ----------------------------------- + ----------------------------- + I*|- ----------------------------------- - -----------------------------------|
123 ________________________ 6 | ________________________ 6 |
/ _________ | / _________ |
/ 378820 3*\/ 9626961 | / 378820 3*\/ 9626961 |
10086*3 / ------ + ------------- | 10086*3 / ------ + ------------- |
\/ 68921 1681 \ \/ 68921 1681 /
$$x_{2} = - \frac{1289}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}} + \frac{8}{123} + \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{6} - \frac{1289 \sqrt{3}}{10086 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}\right)$$
________________________
/ _________
/ 378820 3*\/ 9626961
3 / ------ + -------------
8 \/ 68921 1681 1289
x3 = --- - ----------------------------- + ----------------------------------
123 3 ________________________
/ _________
/ 378820 3*\/ 9626961
5043*3 / ------ + -------------
\/ 68921 1681
$$x_{3} = - \frac{\sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}{3} + \frac{8}{123} + \frac{1289}{5043 \sqrt[3]{\frac{378820}{68921} + \frac{3 \sqrt{9626961}}{1681}}}$$
x3 = -(378820/68921 + 3*sqrt(9626961)/1681)^(1/3)/3 + 8/123 + 1289/(5043*(378820/68921 + 3*sqrt(9626961)/1681)^(1/3))
Respuesta numérica
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x1 = 0.378676256578103 + 0.742094134653283*i
x2 = 0.378676256578103 - 0.742094134653283*i
x3 = -0.562230561936694
x3 = -0.562230561936694