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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2+4=5x
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
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Expresiones idénticas
- (sqrt(x+ cuatro)+sqrt(x+ cuatro))/ dos =x+sqrt(x^(dos)- dieciséis)- seis
- ( raíz cuadrada de (x más 4) más raíz cuadrada de (x más 4)) dividir por 2 es igual a x más raíz cuadrada de (x en el grado (2) menos 16) menos 6
- ( raíz cuadrada de (x más cuatro) más raíz cuadrada de (x más cuatro)) dividir por dos es igual a x más raíz cuadrada de (x en el grado (dos) menos dieciséis) menos seis
- (√(x+4)+√(x+4))/2=x+√(x^(2)-16)-6
- (sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x(2)-16)-6
- sqrtx+4+sqrtx+4/2=x+sqrtx2-16-6
- sqrtx+4+sqrtx+4/2=x+sqrtx^2-16-6
- (sqrt(x+4)+sqrt(x+4)) dividir por 2=x+sqrt(x^(2)-16)-6
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Expresiones semejantes
- (sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)+6
- (sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)+16)-6
- (sqrt(x+4)-sqrt(x+4))/2=x+sqrt(x^(2)-16)-6
- (sqrt(x+4)+sqrt(x+4))/2=x-sqrt(x^(2)-16)-6
- (sqrt(x+4)+sqrt(x-4))/2=x+sqrt(x^(2)-16)-6
- (sqrt(x-4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)-6
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)-6 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_______ _______ _________
\/ x + 4 + \/ x + 4 / 2
--------------------- = x + \/ x - 16 - 6
2
$$\frac{\sqrt{x + 4} + \sqrt{x + 4}}{2} = \left(x + \sqrt{x^{2} - 16}\right) - 6$$
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \
3067*re|-------------------------------------------| |3067*im|-------------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| ______________________| | | ______________________| | |1600*\/ 669 || | |1600*\/ 669 ||| | |1600*\/ 669 || | |1600*\/ 669 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
|| 1 I*\/ 3 | / 32363 25*I*\/ 669 | | || 1 I*\/ 3 | / 32363 25*I*\/ 669 | ______ | \ 291267 /| ______ | \ 291267 /|| ______ | \ 291267 /| ______ | \ 291267 /|
||- - - -------|*3 / ----- + ------------ | | ||- - - -------|*3 / ----- + ------------ | \/ 3067 *cos|------------------| \/ 9201 *sin|------------------|| \/ 9201 *cos|------------------| \/ 3067 *sin|------------------|
51 \\ 2 2 / \/ 64 9 / | \\ 2 2 / \/ 64 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4 48 \ 48 8 24 / 24 8
$$- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)$$
=
/ 1 \ / / 1 \ \
3067*re|-------------------------------------------| |3067*im|-------------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| ______________________| | | ______________________| | |1600*\/ 669 || | |1600*\/ 669 ||| | |1600*\/ 669 || | |1600*\/ 669 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
|| 1 I*\/ 3 | / 32363 25*I*\/ 669 | | || 1 I*\/ 3 | / 32363 25*I*\/ 669 | ______ | \ 291267 /| ______ | \ 291267 /|| ______ | \ 291267 /| ______ | \ 291267 /|
||- - - -------|*3 / ----- + ------------ | | ||- - - -------|*3 / ----- + ------------ | \/ 3067 *cos|------------------| \/ 9201 *sin|------------------|| \/ 9201 *cos|------------------| \/ 3067 *sin|------------------|
51 \\ 2 2 / \/ 64 9 / | \\ 2 2 / \/ 64 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4 48 \ 48 8 24 / 24 8
$$- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)$$
producto
/ 1 \ / / 1 \ \
3067*re|-------------------------------------------| |3067*im|-------------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| ______________________| | | ______________________| | |1600*\/ 669 || | |1600*\/ 669 ||| | |1600*\/ 669 || | |1600*\/ 669 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
|| 1 I*\/ 3 | / 32363 25*I*\/ 669 | | || 1 I*\/ 3 | / 32363 25*I*\/ 669 | ______ | \ 291267 /| ______ | \ 291267 /|| ______ | \ 291267 /| ______ | \ 291267 /|
||- - - -------|*3 / ----- + ------------ | | ||- - - -------|*3 / ----- + ------------ | \/ 3067 *cos|------------------| \/ 9201 *sin|------------------|| \/ 9201 *cos|------------------| \/ 3067 *sin|------------------|
51 \\ 2 2 / \/ 64 9 / | \\ 2 2 / \/ 64 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4 48 \ 48 8 24 / 24 8
$$- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)$$
=
/ / _____\ \
| |1600*\/ 669 | |
| atan|------------| |
______ | \ 291267 / pi|
\/ 9201 *sin|- ------------------ + --|
51 \ 3 6 /
-- - ---------------------------------------
4 6
$$- \frac{\sqrt{9201} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} + \frac{\pi}{6} \right)}}{6} + \frac{51}{4}$$
51/4 - sqrt(9201)*sin(-atan(1600*sqrt(669)/291267)/3 + pi/6)/6
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
3067*re|-------------------------------------------| |3067*im|-------------------------------------------| / / _____\\ / / _____\\| / / _____\\ / / _____\\
| ______________________| | | ______________________| | |1600*\/ 669 || | |1600*\/ 669 ||| | |1600*\/ 669 || | |1600*\/ 669 ||
|/ ___\ / _____ | | |/ ___\ / _____ | |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
|| 1 I*\/ 3 | / 32363 25*I*\/ 669 | | || 1 I*\/ 3 | / 32363 25*I*\/ 669 | ______ | \ 291267 /| ______ | \ 291267 /|| ______ | \ 291267 /| ______ | \ 291267 /|
||- - - -------|*3 / ----- + ------------ | | ||- - - -------|*3 / ----- + ------------ | \/ 3067 *cos|------------------| \/ 9201 *sin|------------------|| \/ 9201 *cos|------------------| \/ 3067 *sin|------------------|
51 \\ 2 2 / \/ 64 9 / | \\ 2 2 / \/ 64 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4 48 \ 48 8 24 / 24 8
$$x_{1} = - \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)$$
x1 = -sqrt(9201)*cos(atan(1600*sqrt(669)/291267)/3)/24 + 3067*re(1/((-1/2 - sqrt(3)*i/2)*(32363/64 + 25*sqrt(669)*i/9)^(1/3)))/48 + sqrt(3067)*sin(atan(1600*sqrt(669)/291267)/3)/8 + 51/4 + i*(-sqrt(3067)*cos(atan(1600*sqrt(669)/291267)/3)/8 - sqrt(9201)*sin(atan(1600*sqrt(669)/291267)/3)/24 + 3067*im(1/((-1/2 - sqrt(3)*i/2)*(32363/64 + 25*sqrt(669)*i/9)^(1/3)))/48)