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La ecuación:
Ecuación 6x+1=-4x
Ecuación x+y-3=0
Ecuación x^2=-3
Ecuación 9-7(x+3)=5-6x
Expresar {x} en función de y en la ecuación:
-11*x+9*y=-20
5*x-14*y=-15
-10*x+15*y=10
-9*x-6*y=12
Expresiones idénticas
sqrt(cinco x/(x+ tres))-(5*sqrt((x+ tres)/5x))= cuatro
raíz cuadrada de (5x dividir por (x más 3)) menos (5 multiplicar por raíz cuadrada de ((x más 3) dividir por 5x)) es igual a 4
raíz cuadrada de (cinco x dividir por (x más tres)) menos (5 multiplicar por raíz cuadrada de ((x más tres) dividir por 5x)) es igual a cuatro
√(5x/(x+3))-(5*√((x+3)/5x))=4
sqrt(5x/(x+3))-(5sqrt((x+3)/5x))=4
sqrt5x/x+3-5sqrtx+3/5x=4
sqrt(5x dividir por (x+3))-(5*sqrt((x+3) dividir por 5x))=4
Expresiones semejantes
sqrt(5x/(x+3))-(5*sqrt((x-3)/5x))=4
sqrt(5x/(x-3))-(5*sqrt((x+3)/5x))=4
sqrt(5x/(x+3))+(5*sqrt((x+3)/5x))=4
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(0*x+0)=0
sqrt(1-x)=sqrt[3](x-2)
sqrt(x-1)+sqrt(3-x)=2
sqrt(x)^1=0
sqrt(10x+11)=-x
Raíz cuadrada sqrt
sqrt(0*x+0)=0
sqrt(1-x)=sqrt[3](x-2)
sqrt(x-1)+sqrt(3-x)=2
sqrt(x)^1=0
sqrt(10x+11)=-x

sqrt(5x/(x+3))-(5*sqrt((x+3)/5x))=4 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

    _______         _________    
   /  5*x          / x + 3       
  /  -----  - 5*  /  -----*x  = 4
\/   x + 3      \/     5

- 5 \sqrt{x \frac{x + 3}{5}} + \sqrt{\frac{5 x}{x + 3}} = 4

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                 /                    1                     \     /      /                    1                     \                                                                    \                                                                    
           128*re|------------------------------------------|     |128*im|------------------------------------------|               /    /    _______\\               /    /    _______\\|               /    /    _______\\               /    /    _______\\
                 |                     _____________________|     |      |                     _____________________|               |    |3*\/ 11535 ||               |    |3*\/ 11535 |||               |    |3*\/ 11535 ||               |    |3*\/ 11535 ||
                 |/          ___\     /             _______ |     |      |/          ___\     /             _______ |               |atan|-----------||               |atan|-----------|||               |atan|-----------||               |atan|-----------||
                 ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |     |      ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |       ____    |    \    245    /|       ____    |    \    245    /||       ____    |    \    245    /|       ____    |    \    245    /|
                 ||- - - -------|*3 /   --- + ------------- |     |      ||- - - -------|*3 /   --- + ------------- |   4*\/ 10 *sin|-----------------|   4*\/ 30 *cos|-----------------||   4*\/ 10 *cos|-----------------|   4*\/ 30 *sin|-----------------|
       8         \\  2      2   / \/    135        225      /     |      \\  2      2   / \/    135        225      /               \        3        /               \        3        /|               \        3        /               \        3        /
x1 = - - + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------- - -------------------------------| - ------------------------------- + -------------------------------
       3                           45                             \                        45                                          15                                15              /                  15                                15

x_{1} = - \frac{8}{3} - \frac{4 \sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45} + \frac{4 \sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + i \left(- \frac{4 \sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} - \frac{4 \sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45}\right)

x1 = -8/3 - 4*sqrt(10)*cos(atan(3*sqrt(11535)/245)/3)/15 + 128*re(1/((-1/2 - sqrt(3)*i/2)*(392/135 + 8*sqrt(11535)*i/225)^(1/3)))/45 + 4*sqrt(30)*sin(atan(3*sqrt(11535)/245)/3)/15 + i*(-4*sqrt(30)*cos(atan(3*sqrt(11535)/245)/3)/15 - 4*sqrt(10)*sin(atan(3*sqrt(11535)/245)/3)/15 + 128*im(1/((-1/2 - sqrt(3)*i/2)*(392/135 + 8*sqrt(11535)*i/225)^(1/3)))/45)

Suma y producto de raíces [src]

suma

            /                    1                     \     /      /                    1                     \                                                                    \                                                                    
      128*re|------------------------------------------|     |128*im|------------------------------------------|               /    /    _______\\               /    /    _______\\|               /    /    _______\\               /    /    _______\\
            |                     _____________________|     |      |                     _____________________|               |    |3*\/ 11535 ||               |    |3*\/ 11535 |||               |    |3*\/ 11535 ||               |    |3*\/ 11535 ||
            |/          ___\     /             _______ |     |      |/          ___\     /             _______ |               |atan|-----------||               |atan|-----------|||               |atan|-----------||               |atan|-----------||
            ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |     |      ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |       ____    |    \    245    /|       ____    |    \    245    /||       ____    |    \    245    /|       ____    |    \    245    /|
            ||- - - -------|*3 /   --- + ------------- |     |      ||- - - -------|*3 /   --- + ------------- |   4*\/ 10 *sin|-----------------|   4*\/ 30 *cos|-----------------||   4*\/ 10 *cos|-----------------|   4*\/ 30 *sin|-----------------|
  8         \\  2      2   / \/    135        225      /     |      \\  2      2   / \/    135        225      /               \        3        /               \        3        /|               \        3        /               \        3        /
- - + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------- - -------------------------------| - ------------------------------- + -------------------------------
  3                           45                             \                        45                                          15                                15              /                  15                                15

- \frac{8}{3} - \frac{4 \sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45} + \frac{4 \sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + i \left(- \frac{4 \sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} - \frac{4 \sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45}\right)

            /                    1                     \     /      /                    1                     \                                                                    \                                                                    
      128*re|------------------------------------------|     |128*im|------------------------------------------|               /    /    _______\\               /    /    _______\\|               /    /    _______\\               /    /    _______\\
            |                     _____________________|     |      |                     _____________________|               |    |3*\/ 11535 ||               |    |3*\/ 11535 |||               |    |3*\/ 11535 ||               |    |3*\/ 11535 ||
            |/          ___\     /             _______ |     |      |/          ___\     /             _______ |               |atan|-----------||               |atan|-----------|||               |atan|-----------||               |atan|-----------||
            ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |     |      ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |       ____    |    \    245    /|       ____    |    \    245    /||       ____    |    \    245    /|       ____    |    \    245    /|
            ||- - - -------|*3 /   --- + ------------- |     |      ||- - - -------|*3 /   --- + ------------- |   4*\/ 10 *sin|-----------------|   4*\/ 30 *cos|-----------------||   4*\/ 10 *cos|-----------------|   4*\/ 30 *sin|-----------------|
  8         \\  2      2   / \/    135        225      /     |      \\  2      2   / \/    135        225      /               \        3        /               \        3        /|               \        3        /               \        3        /
- - + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------- - -------------------------------| - ------------------------------- + -------------------------------
  3                           45                             \                        45                                          15                                15              /                  15                                15

- \frac{8}{3} - \frac{4 \sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45} + \frac{4 \sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + i \left(- \frac{4 \sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} - \frac{4 \sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45}\right)

producto

            /                    1                     \     /      /                    1                     \                                                                    \                                                                    
      128*re|------------------------------------------|     |128*im|------------------------------------------|               /    /    _______\\               /    /    _______\\|               /    /    _______\\               /    /    _______\\
            |                     _____________________|     |      |                     _____________________|               |    |3*\/ 11535 ||               |    |3*\/ 11535 |||               |    |3*\/ 11535 ||               |    |3*\/ 11535 ||
            |/          ___\     /             _______ |     |      |/          ___\     /             _______ |               |atan|-----------||               |atan|-----------|||               |atan|-----------||               |atan|-----------||
            ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |     |      ||  1   I*\/ 3 |    /  392   8*I*\/ 11535  |       ____    |    \    245    /|       ____    |    \    245    /||       ____    |    \    245    /|       ____    |    \    245    /|
            ||- - - -------|*3 /   --- + ------------- |     |      ||- - - -------|*3 /   --- + ------------- |   4*\/ 10 *sin|-----------------|   4*\/ 30 *cos|-----------------||   4*\/ 10 *cos|-----------------|   4*\/ 30 *sin|-----------------|
  8         \\  2      2   / \/    135        225      /     |      \\  2      2   / \/    135        225      /               \        3        /               \        3        /|               \        3        /               \        3        /
- - + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------- - -------------------------------| - ------------------------------- + -------------------------------
  3                           45                             \                        45                                          15                                15              /                  15                                15

- \frac{8}{3} - \frac{4 \sqrt{10} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45} + \frac{4 \sqrt{30} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + i \left(- \frac{4 \sqrt{30} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} - \frac{4 \sqrt{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} \right)}}{15} + \frac{128 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{392}{135} + \frac{8 \sqrt{11535} i}{225}}}\right)}}{45}\right)

                   /      /    _______\     \
                   |      |3*\/ 11535 |     |
                   |  atan|-----------|     |
           ____    |      \    245    /   pi|
      16*\/ 10 *sin|- ----------------- + --|
  8                \          3           6 /
- - - ---------------------------------------
  3                      15

- \frac{8}{3} - \frac{16 \sqrt{10} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{11535}}{245} \right)}}{3} + \frac{\pi}{6} \right)}}{15}

-8/3 - 16*sqrt(10)*sin(-atan(3*sqrt(11535)/245)/3 + pi/6)/15

Respuesta numérica [src]

x1 = -3.3919281523806

x1 = -3.3919281523806

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

sqrt(5x/(x+3))-(5*sqrt((x+3)/5x))=4 la ecuación

Solución numérica:

Solución