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- La ecuación:
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Ecuación x+9=0
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Ecuación 2x^2+7x-9=0
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Ecuación 5*x^2+9*x=0
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Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -14*x+4*y=-16
- 11*x-9*y=-4
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Expresiones idénticas
- *x^ dos + quince *x+ dos *sqrt(x^ dos + cinco *x+ uno)= dos
- multiplicar por x al cuadrado más 15 multiplicar por x más 2 multiplicar por raíz cuadrada de (x al cuadrado más 5 multiplicar por x más 1) es igual a 2
- multiplicar por x en el grado dos más quince multiplicar por x más dos multiplicar por raíz cuadrada de (x en el grado dos más cinco multiplicar por x más uno) es igual a dos
- *x^2+15*x+2*√(x^2+5*x+1)=2
- *x2+15*x+2*sqrt(x2+5*x+1)=2
- *x2+15*x+2*sqrtx2+5*x+1=2
- *x²+15*x+2*sqrt(x²+5*x+1)=2
- *x en el grado 2+15*x+2*sqrt(x en el grado 2+5*x+1)=2
- x^2+15x+2sqrt(x^2+5x+1)=2
- x2+15x+2sqrt(x2+5x+1)=2
- x2+15x+2sqrtx2+5x+1=2
- x^2+15x+2sqrtx^2+5x+1=2
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Expresiones semejantes
- *x^2+15*x-2*sqrt(x^2+5*x+1)=2
- *x^2-15*x+2*sqrt(x^2+5*x+1)=2
- *x^2+15*x+2*sqrt(x^2-5*x+1)=2
- *x^2+15*x+2*sqrt(x^2+5*x-1)=2
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-3)+sqrt(5-x)=2
- sqrt(x^2-4*x+4)-3=0
- sqrt(14*14+14*14)=x
- sqrt(5*x+5)-sqrt(3-3*x)=2*sqrt(x)
- sqrt2x=(1-x)
*x^2+15*x+2*sqrt(x^2+5*x+1)=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
______________ 2 / 2 x + 15*x + 2*\/ x + 5*x + 1 = 2
$$\left(x^{2} + 15 x\right) + 2 \sqrt{\left(x^{2} + 5 x\right) + 1} = 2$$
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \
83*re|-------------------------------------------| |83*im|-------------------------------------------| / / ________\\ / / ________\\| / / ________\\ / / ________\\
| ______________________ | | | ______________________ | | |2*\/ 112434 || | |2*\/ 112434 ||| | |2*\/ 112434 || | |2*\/ 112434 ||
| / ________ / ___\| | | / ________ / ___\| |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
| / 2*I*\/ 112434 | 1 I*\/ 3 || | | / 2*I*\/ 112434 | 1 I*\/ 3 || ____ | \ 1125 /| _____ | \ 1125 /|| ____ | \ 1125 /| _____ | \ 1125 /|
|3 / 125 + -------------- *|- - - -------|| | |3 / 125 + -------------- *|- - - -------|| \/ 83 *cos|------------------| \/ 249 *sin|------------------|| \/ 83 *sin|------------------| \/ 249 *cos|------------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
3 \ 3 2 6 / 2 6
$$-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)$$
=
/ 1 \ / / 1 \ \
83*re|-------------------------------------------| |83*im|-------------------------------------------| / / ________\\ / / ________\\| / / ________\\ / / ________\\
| ______________________ | | | ______________________ | | |2*\/ 112434 || | |2*\/ 112434 ||| | |2*\/ 112434 || | |2*\/ 112434 ||
| / ________ / ___\| | | / ________ / ___\| |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
| / 2*I*\/ 112434 | 1 I*\/ 3 || | | / 2*I*\/ 112434 | 1 I*\/ 3 || ____ | \ 1125 /| _____ | \ 1125 /|| ____ | \ 1125 /| _____ | \ 1125 /|
|3 / 125 + -------------- *|- - - -------|| | |3 / 125 + -------------- *|- - - -------|| \/ 83 *cos|------------------| \/ 249 *sin|------------------|| \/ 83 *sin|------------------| \/ 249 *cos|------------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
3 \ 3 2 6 / 2 6
$$-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)$$
producto
/ / 1 \ / / 1 \ \ \ | 83*re|-------------------------------------------| |83*im|-------------------------------------------| / / ________\\ / / ________\\| / / ________\\ / / ________\\| | | ______________________ | | | ______________________ | | |2*\/ 112434 || | |2*\/ 112434 ||| | |2*\/ 112434 || | |2*\/ 112434 ||| | | / ________ / ___\| | | / ________ / ___\| |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||| | | / 2*I*\/ 112434 | 1 I*\/ 3 || | | / 2*I*\/ 112434 | 1 I*\/ 3 || ____ | \ 1125 /| _____ | \ 1125 /|| ____ | \ 1125 /| _____ | \ 1125 /|| | |3 / 125 + -------------- *|- - - -------|| | |3 / 125 + -------------- *|- - - -------|| \/ 83 *cos|------------------| \/ 249 *sin|------------------|| \/ 83 *sin|------------------| \/ 249 *cos|------------------|| | \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| 0*|-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------| \ 3 \ 3 2 6 / 2 6 /
$$0 \left(-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
/ 1 \ / / 1 \ \
83*re|-------------------------------------------| |83*im|-------------------------------------------| / / ________\\ / / ________\\| / / ________\\ / / ________\\
| ______________________ | | | ______________________ | | |2*\/ 112434 || | |2*\/ 112434 ||| | |2*\/ 112434 || | |2*\/ 112434 ||
| / ________ / ___\| | | / ________ / ___\| |atan|------------|| |atan|------------||| |atan|------------|| |atan|------------||
| / 2*I*\/ 112434 | 1 I*\/ 3 || | | / 2*I*\/ 112434 | 1 I*\/ 3 || ____ | \ 1125 /| _____ | \ 1125 /|| ____ | \ 1125 /| _____ | \ 1125 /|
|3 / 125 + -------------- *|- - - -------|| | |3 / 125 + -------------- *|- - - -------|| \/ 83 *cos|------------------| \/ 249 *sin|------------------|| \/ 83 *sin|------------------| \/ 249 *cos|------------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
3 \ 3 2 6 / 2 6
$$x_{2} = -10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)$$
x2 = -10 - sqrt(249)*cos(atan(2*sqrt(112434)/1125)/3)/6 + 83*re(1/((-1/2 - sqrt(3)*i/2)*(125 + 2*sqrt(112434)*i/9)^(1/3)))/3 + sqrt(83)*sin(atan(2*sqrt(112434)/1125)/3)/2 + i*(-sqrt(83)*cos(atan(2*sqrt(112434)/1125)/3)/2 - sqrt(249)*sin(atan(2*sqrt(112434)/1125)/3)/6 + 83*im(1/((-1/2 - sqrt(3)*i/2)*(125 + 2*sqrt(112434)*i/9)^(1/3)))/3)