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- La ecuación:
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Ecuación x^2+5x=36
-
Ecuación 3*x-6=x+4
-
Ecuación 9^x-8*3^x-9=0
-
Ecuación x^3+4=0
- Expresar {x} en función de y en la ecuación:
- -2*x-19*y=3
- 6*x+17*y=-11
- -11*x-7*y=-2
- -19*x+14*y=20
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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
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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
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- 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
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- 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(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
$$- 5 \sqrt{x \frac{x + 3}{5}} + \sqrt{\frac{5 x}{x + 3}} = 4$$
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