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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
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Expresiones idénticas
- sqrt((cuatro *x^ dos)- uno)= uno -sqrt((cuatro *x)- uno)
- raíz cuadrada de ((4 multiplicar por x al cuadrado ) menos 1) es igual a 1 menos raíz cuadrada de ((4 multiplicar por x) menos 1)
- raíz cuadrada de ((cuatro multiplicar por x en el grado dos) menos uno) es igual a uno menos raíz cuadrada de ((cuatro multiplicar por x) menos uno)
- √((4*x^2)-1)=1-√((4*x)-1)
- sqrt((4*x2)-1)=1-sqrt((4*x)-1)
- sqrt4*x2-1=1-sqrt4*x-1
- sqrt((4*x²)-1)=1-sqrt((4*x)-1)
- sqrt((4*x en el grado 2)-1)=1-sqrt((4*x)-1)
- sqrt((4x^2)-1)=1-sqrt((4x)-1)
- sqrt((4x2)-1)=1-sqrt((4x)-1)
- sqrt4x2-1=1-sqrt4x-1
- sqrt4x^2-1=1-sqrt4x-1
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Expresiones semejantes
- sqrt((4*x^2)+1)=1-sqrt((4*x)-1)
- sqrt((4*x^2)-1)=1-sqrt((4*x)+1)
- sqrt((4*x^2)-1)=1+sqrt((4*x)-1)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+4)=x-3
- sqrt(6+5*x)=x
- sqrt(3+2*x)=x
- sqrt(x+1)=x-5
- sqrt(x^2-5x+1)=sqrt(x-4)
- Raíz cuadrada sqrt
- sqrt(x+4)=x-3
- sqrt(6+5*x)=x
- sqrt(3+2*x)=x
- sqrt(x+1)=x-5
- sqrt(x^2-5x+1)=sqrt(x-4)
sqrt((4*x^2)-1)=1-sqrt((4*x)-1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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__________ / 2 _________ \/ 4*x - 1 = 1 - \/ 4*x - 1
$$\sqrt{4 x^{2} - 1} = 1 - \sqrt{4 x - 1}$$
Suma y producto de raíces
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suma
____________ / ____________ \ ____________ / ____________ \
/ ____ | / ____ | / ____ | / ____ |
/ 1 \/ 69 | ___ / 1 \/ 69 | / 1 \/ 69 | ___ / 1 \/ 69 |
3 / - + ------ | \/ 3 *3 / - + ------ ___ | 3 / - + ------ |\/ 3 *3 / - + ------ ___ |
1 1 \/ 2 18 1 | \/ 2 18 \/ 3 | 1 \/ 2 18 1 | \/ 2 18 \/ 3 |
- + - - ----------------- - ------------------- + I*|- ----------------------- + -------------------| + - - ----------------- - ------------------- + I*|----------------------- - -------------------|
2 2 2 ____________ | 2 ____________| 2 2 ____________ | 2 ____________|
/ ____ | / ____ | / ____ | / ____ |
/ 1 \/ 69 | / 1 \/ 69 | / 1 \/ 69 | / 1 \/ 69 |
6*3 / - + ------ | 6*3 / - + ------ | 6*3 / - + ------ | 6*3 / - + ------ |
\/ 2 18 \ \/ 2 18 / \/ 2 18 \ \/ 2 18 /
$$\left(\frac{1}{2} + \left(- \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}\right)\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2}\right)\right)$$
=
/ ____________ \ / ____________ \
| / ____ | | / ____ |
____________ | ___ / 1 \/ 69 | | ___ / 1 \/ 69 |
/ ____ |\/ 3 *3 / - + ------ ___ | | \/ 3 *3 / - + ------ ___ |
3 / 1 \/ 69 1 | \/ 2 18 \/ 3 | | \/ 2 18 \/ 3 |
- - 3 / - + ------ - ------------------- + I*|----------------------- - -------------------| + I*|- ----------------------- + -------------------|
2 \/ 2 18 ____________ | 2 ____________| | 2 ____________|
/ ____ | / ____ | | / ____ |
/ 1 \/ 69 | / 1 \/ 69 | | / 1 \/ 69 |
3*3 / - + ------ | 6*3 / - + ------ | | 6*3 / - + ------ |
\/ 2 18 \ \/ 2 18 / \ \/ 2 18 /
$$- \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}} - \frac{1}{3 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{3}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}\right) + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2}\right)$$
producto
____________ / ____________ \
/ ____ | / ____ |
/ 1 \/ 69 | ___ / 1 \/ 69 |
3 / - + ------ | \/ 3 *3 / - + ------ ___ |
1 \/ 2 18 1 | \/ 2 18 \/ 3 |
- - ----------------- - ------------------- + I*|- ----------------------- + -------------------|
2 2 ____________ | 2 ____________| / ____________ / ____________ \\
/ ____ | / ____ | | / ____ | / ____ ||
/ 1 \/ 69 | / 1 \/ 69 | | / 1 \/ 69 | ___ / 1 \/ 69 ||
6*3 / - + ------ | 6*3 / - + ------ | | 3 / - + ------ |\/ 3 *3 / - + ------ ___ ||
\/ 2 18 \ \/ 2 18 / |1 \/ 2 18 1 | \/ 2 18 \/ 3 ||
-------------------------------------------------------------------------------------------------*|- - ----------------- - ------------------- + I*|----------------------- - -------------------||
2 |2 2 ____________ | 2 ____________||
| / ____ | / ____ ||
| / 1 \/ 69 | / 1 \/ 69 ||
| 6*3 / - + ------ | 6*3 / - + ------ ||
\ \/ 2 18 \ \/ 2 18 //
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2}\right)\right) \frac{- \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}\right)}{2}$$
=
2/3 _________________ _______________ _______________
3 ____ / ____\ 3 / ____ 2/3 3 ___ 2/3 3 / ____ 2/3 5/6 ____ 6 ___ ____ 3 / ____
\/ 12 \9 + \/ 69 / \/ 162 + 18*\/ 69 2 *\/ 3 3*3 *\/ 18 + 2*\/ 69 2 *3 *\/ 23 \/ 3 *\/ 23 *\/ 18 + 2*\/ 69
- ------ - --------------- - -------------------- + ---------- + ------------------------- - ---------------- + -------------------------------
3 24 48 8 16 24 12
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2/3
/ ____\
\9 + \/ 69 /
$$\frac{- \frac{2^{\frac{2}{3}} \sqrt{23} \cdot 3^{\frac{5}{6}}}{24} - \frac{\sqrt[3]{12}}{3} - \frac{\left(\sqrt{69} + 9\right)^{\frac{2}{3}}}{24} - \frac{\sqrt[3]{18 \sqrt{69} + 162}}{48} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{8} + \frac{3 \cdot 3^{\frac{2}{3}} \sqrt[3]{2 \sqrt{69} + 18}}{16} + \frac{\sqrt{23} \sqrt[6]{3} \sqrt[3]{2 \sqrt{69} + 18}}{12}}{\left(\sqrt{69} + 9\right)^{\frac{2}{3}}}$$
(-12^(1/3)/3 - (9 + sqrt(69))^(2/3)/24 - (162 + 18*sqrt(69))^(1/3)/48 + 2^(2/3)*3^(1/3)/8 + 3*3^(2/3)*(18 + 2*sqrt(69))^(1/3)/16 - 2^(2/3)*3^(5/6)*sqrt(23)/24 + 3^(1/6)*sqrt(23)*(18 + 2*sqrt(69))^(1/3)/12)/(9 + sqrt(69))^(2/3)
Respuesta rápida
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x1 = 1/2
$$x_{1} = \frac{1}{2}$$
____________ / ____________ \
/ ____ | / ____ |
/ 1 \/ 69 | ___ / 1 \/ 69 |
3 / - + ------ | \/ 3 *3 / - + ------ ___ |
1 \/ 2 18 1 | \/ 2 18 \/ 3 |
x2 = - - ----------------- - ------------------- + I*|- ----------------------- + -------------------|
2 2 ____________ | 2 ____________|
/ ____ | / ____ |
/ 1 \/ 69 | / 1 \/ 69 |
6*3 / - + ------ | 6*3 / - + ------ |
\/ 2 18 \ \/ 2 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}\right)$$
____________ / ____________ \
/ ____ | / ____ |
/ 1 \/ 69 | ___ / 1 \/ 69 |
3 / - + ------ |\/ 3 *3 / - + ------ ___ |
1 \/ 2 18 1 | \/ 2 18 \/ 3 |
x3 = - - ----------------- - ------------------- + I*|----------------------- - -------------------|
2 2 ____________ | 2 ____________|
/ ____ | / ____ |
/ 1 \/ 69 | / 1 \/ 69 |
6*3 / - + ------ | 6*3 / - + ------ |
\/ 2 18 \ \/ 2 18 /
$$x_{3} = - \frac{\sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2} - \frac{1}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{1}{2} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{69}}{18} + \frac{1}{2}}}{2}\right)$$
x3 = -(sqrt(69)/18 + 1/2)^(1/3)/2 - 1/(6*(sqrt(69)/18 + 1/2)^(1/3)) + 1/2 + i*(-sqrt(3)/(6*(sqrt(69)/18 + 1/2)^(1/3)) + sqrt(3)*(sqrt(69)/18 + 1/2)^(1/3)/2)
Respuesta numérica
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x1 = 0.5
x2 = -0.162358978622373 - 0.562279512062301*i
x3 = -0.162358978622373 + 0.562279512062301*i
x3 = -0.162358978622373 + 0.562279512062301*i