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- La ecuación:
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Ecuación x^2+5x=36
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
-
Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
-
Expresiones idénticas
- sqrt(sqrt(x- seis))+sqrt(seis -x)= uno
- raíz cuadrada de ( raíz cuadrada de (x menos 6)) más raíz cuadrada de (6 menos x) es igual a 1
- raíz cuadrada de ( raíz cuadrada de (x menos seis)) más raíz cuadrada de (seis menos x) es igual a uno
- √(√(x-6))+√(6-x)=1
- sqrtsqrtx-6+sqrt6-x=1
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Expresiones semejantes
- sqrt(sqrt(x+6))+sqrt(6-x)=1
- sqrt(sqrt(x-6))-sqrt(6-x)=1
- sqrt(sqrt(x-6))+sqrt(6+x)=1
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
- sqrt(3*x+1)=x-1
- Raíz cuadrada sqrt
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
- sqrt(3*x+1)=x-1
- Raíz cuadrada sqrt
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
- sqrt(3*x+1)=x-1
sqrt(sqrt(x-6))+sqrt(6-x)=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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___________ / _______ _______ \/ \/ x - 6 + \/ 6 - x = 1
$$\sqrt{6 - x} + \sqrt{\sqrt{x - 6}} = 1$$
Suma y producto de raíces
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suma
2 2
/ / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\ / / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\
4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------|| 4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------||
/ 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ | 1 \ 2 /| / 4 ____ /atan(4)\\ | ____ | 1 \ 2 /| 2/atan(4)\ / 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ |1 \ 2 /| / 4 ____ /atan(4)\\ | ____ |1 \ 2 /| 2/atan(4)\
| \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - + -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - + -------------------| *sin |-------| | \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - -------------------| *sin |-------|
| 1 \ 2 /| \ 2 / | \ 2 / \ 2 2 / 4 ____ |1 \ 2 /| /atan(4)\| \ 2 2 / \ 2 / |1 \ 2 /| \ 2 / | \ 2 / \2 2 / 4 ____ | 1 \ 2 /| /atan(4)\| \2 2 / \ 2 /
6 + |- - + -------------------| + ---------------- + I*|----------------------------------------------- + 2*\/ 17 *|- - -------------------| *sin|-------|| - --------------------------------------------------- + 6 + |- - -------------------| + ---------------- + I*|--------------------------------------------- + 2*\/ 17 *|- - + -------------------| *sin|-------|| - -------------------------------------------------
\ 2 2 / 16 \ 2 \2 2 / \ 2 // 2 \2 2 / 16 \ 2 \ 2 2 / \ 2 // 2
$$\left(- \frac{3 \sqrt{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(\frac{17^{\frac{3}{4}} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + 2 \sqrt[4]{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}\right)\right) + \left(- \frac{3 \sqrt{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(2 \sqrt[4]{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} + \frac{17^{\frac{3}{4}} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)\right)$$
=
2 2
/ / 4 ____ /atan(4)\\ \ / / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\ / 4 ____ /atan(4)\\
4 4 | | \/ 17 *cos|-------|| 3 | | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------|| | \/ 17 *cos|-------||
/ 4 ____ /atan(4)\\ / 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ |1 \ 2 /| / 4 ____ /atan(4)\\ | | 3/4 3/atan(4)\ | 1 \ 2 /| / 4 ____ /atan(4)\\ | ____ |1 \ 2 /| 2/atan(4)\ ____ | 1 \ 2 /| 2/atan(4)\
| \/ 17 *cos|-------|| | \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - -------------------| | \/ 17 *cos|-------|| | |17 *sin |-------|*|- - + -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - -------------------| *sin |-------| 3*\/ 17 *|- - + -------------------| *sin |-------|
|1 \ 2 /| | 1 \ 2 /| \ 2 / | \ 2 / \2 2 / 4 ____ | 1 \ 2 /| /atan(4)\| | \ 2 / \ 2 2 / 4 ____ |1 \ 2 /| /atan(4)\| \2 2 / \ 2 / \ 2 2 / \ 2 /
12 + |- - -------------------| + |- - + -------------------| + ---------------- + I*|--------------------------------------------- + 2*\/ 17 *|- - + -------------------| *sin|-------|| + I*|----------------------------------------------- + 2*\/ 17 *|- - -------------------| *sin|-------|| - ------------------------------------------------- - ---------------------------------------------------
\2 2 / \ 2 2 / 8 \ 2 \ 2 2 / \ 2 // \ 2 \2 2 / \ 2 // 2 2
$$- \frac{3 \sqrt{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} - \frac{3 \sqrt{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{4} + \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{8} + 12 + i \left(\frac{17^{\frac{3}{4}} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + 2 \sqrt[4]{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}\right) + i \left(2 \sqrt[4]{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} + \frac{17^{\frac{3}{4}} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)$$
producto
/ 2 \ / 2 \ | / / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\ | | / / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\ | | 4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------|| | | 4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------|| | | / 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ | 1 \ 2 /| / 4 ____ /atan(4)\\ | ____ | 1 \ 2 /| 2/atan(4)\| | / 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ |1 \ 2 /| / 4 ____ /atan(4)\\ | ____ |1 \ 2 /| 2/atan(4)\| | | \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - + -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - + -------------------| *sin |-------|| | | \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - -------------------| *sin |-------|| | | 1 \ 2 /| \ 2 / | \ 2 / \ 2 2 / 4 ____ |1 \ 2 /| /atan(4)\| \ 2 2 / \ 2 /| | |1 \ 2 /| \ 2 / | \ 2 / \2 2 / 4 ____ | 1 \ 2 /| /atan(4)\| \2 2 / \ 2 /| |6 + |- - + -------------------| + ---------------- + I*|----------------------------------------------- + 2*\/ 17 *|- - -------------------| *sin|-------|| - ---------------------------------------------------|*|6 + |- - -------------------| + ---------------- + I*|--------------------------------------------- + 2*\/ 17 *|- - + -------------------| *sin|-------|| - -------------------------------------------------| \ \ 2 2 / 16 \ 2 \2 2 / \ 2 // 2 / \ \2 2 / 16 \ 2 \ 2 2 / \ 2 // 2 /
$$\left(- \frac{3 \sqrt{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(2 \sqrt[4]{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} + \frac{17^{\frac{3}{4}} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{3 \sqrt{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(\frac{17^{\frac{3}{4}} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + 2 \sqrt[4]{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}\right)\right)$$
=
4 ____ /atan(4)\ 3/4 /atan(4)\
____ 33*\/ 17 *cos|-------| 11*17 *cos|-------|
137 5*\/ 17 3/4 /atan(4)\ 4 ____ /atan(4)\ \ 2 / \ 2 /
--- + -------- - 17 *sin|-------| - 3*\/ 17 *sin|-------| - ---------------------- + ---------------------
4 4 \ 2 / \ 2 / 4 4
$$- \frac{33 \sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{4} - 17^{\frac{3}{4}} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} - 3 \sqrt[4]{17} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} + \frac{5 \sqrt{17}}{4} + \frac{11 \cdot 17^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{4} + \frac{137}{4}$$
137/4 + 5*sqrt(17)/4 - 17^(3/4)*sin(atan(4)/2) - 3*17^(1/4)*sin(atan(4)/2) - 33*17^(1/4)*cos(atan(4)/2)/4 + 11*17^(3/4)*cos(atan(4)/2)/4
Respuesta rápida
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2
/ / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\
4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------||
/ 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ | 1 \ 2 /| / 4 ____ /atan(4)\\ | ____ | 1 \ 2 /| 2/atan(4)\
| \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - + -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - + -------------------| *sin |-------|
| 1 \ 2 /| \ 2 / | \ 2 / \ 2 2 / 4 ____ |1 \ 2 /| /atan(4)\| \ 2 2 / \ 2 /
x1 = 6 + |- - + -------------------| + ---------------- + I*|----------------------------------------------- + 2*\/ 17 *|- - -------------------| *sin|-------|| - ---------------------------------------------------
\ 2 2 / 16 \ 2 \2 2 / \ 2 // 2
$$x_{1} = - \frac{3 \sqrt{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(2 \sqrt[4]{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)} + \frac{17^{\frac{3}{4}} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)$$
2
/ / 4 ____ /atan(4)\\ \ / 4 ____ /atan(4)\\
4 | | \/ 17 *cos|-------|| 3 | | \/ 17 *cos|-------||
/ 4 ____ /atan(4)\\ 4/atan(4)\ | 3/4 3/atan(4)\ |1 \ 2 /| / 4 ____ /atan(4)\\ | ____ |1 \ 2 /| 2/atan(4)\
| \/ 17 *cos|-------|| 17*sin |-------| |17 *sin |-------|*|- - -------------------| | \/ 17 *cos|-------|| | 3*\/ 17 *|- - -------------------| *sin |-------|
|1 \ 2 /| \ 2 / | \ 2 / \2 2 / 4 ____ | 1 \ 2 /| /atan(4)\| \2 2 / \ 2 /
x2 = 6 + |- - -------------------| + ---------------- + I*|--------------------------------------------- + 2*\/ 17 *|- - + -------------------| *sin|-------|| - -------------------------------------------------
\2 2 / 16 \ 2 \ 2 2 / \ 2 // 2
$$x_{2} = - \frac{3 \sqrt{17} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{2} \sin^{2}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right)^{4} + \frac{17 \sin^{4}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{16} + 6 + i \left(\frac{17^{\frac{3}{4}} \left(- \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + \frac{1}{2}\right) \sin^{3}{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2} + 2 \sqrt[4]{17} \left(- \frac{1}{2} + \frac{\sqrt[4]{17} \cos{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}}{2}\right)^{3} \sin{\left(\frac{\operatorname{atan}{\left(4 \right)}}{2} \right)}\right)$$
x2 = -3*sqrt(17)*(-17^(1/4)*cos(atan(4)/2)/2 + 1/2)^2*sin(atan(4)/2)^2/2 + (-17^(1/4)*cos(atan(4)/2)/2 + 1/2)^4 + 17*sin(atan(4)/2)^4/16 + 6 + i*(17^(3/4)*(-17^(1/4)*cos(atan(4)/2)/2 + 1/2)*sin(atan(4)/2)^3/2 + 2*17^(1/4)*(-1/2 + 17^(1/4)*cos(atan(4)/2)/2)^3*sin(atan(4)/2))
Respuesta numérica
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x1 = 5.94937847746753 + 0.225295714284067*i
x2 = 5.94937847746753 - 0.225295714284067*i
x2 = 5.94937847746753 - 0.225295714284067*i