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sqrt(x-5)+sqrt(5-x)=3x+2x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  _______     _______            
\/ x - 5  + \/ 5 - x  = 3*x + 2*x
5−x+x−5=2x+3x\sqrt{5 - x} + \sqrt{x - 5} = 2 x + 3 x
Simplificar
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  /       4 _______    /atan(250)\\   4 _______    /atan(250)\     /     4 _______    /atan(250)\\   4 _______    /atan(250)\
  |       \/ 62501 *cos|---------||   \/ 62501 *sin|---------|     |     \/ 62501 *cos|---------||   \/ 62501 *sin|---------|
  |  1                 \    2    /|                \    2    /     |1                 \    2    /|                \    2    /
I*|- -- + ------------------------| + ------------------------ + I*|-- - ------------------------| + ------------------------
  \  25              25           /              25                \25              25           /              25
(625014sin⁡(atan⁡(250)2)25+i(−625014cos⁡(atan⁡(250)2)25+125))+(625014sin⁡(atan⁡(250)2)25+i(−125+625014cos⁡(atan⁡(250)2)25))\left(\frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + \frac{1}{25}\right)\right) + \left(\frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{1}{25} + \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25}\right)\right) 
=
  /       4 _______    /atan(250)\\     /     4 _______    /atan(250)\\     4 _______    /atan(250)\
  |       \/ 62501 *cos|---------||     |     \/ 62501 *cos|---------||   2*\/ 62501 *sin|---------|
  |  1                 \    2    /|     |1                 \    2    /|                  \    2    /
I*|- -- + ------------------------| + I*|-- - ------------------------| + --------------------------
  \  25              25           /     \25              25           /               25
2625014sin⁡(atan⁡(250)2)25+i(−625014cos⁡(atan⁡(250)2)25+125)+i(−125+625014cos⁡(atan⁡(250)2)25)\frac{2 \sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + \frac{1}{25}\right) + i \left(- \frac{1}{25} + \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25}\right) 
producto
/  /       4 _______    /atan(250)\\   4 _______    /atan(250)\\ /  /     4 _______    /atan(250)\\   4 _______    /atan(250)\\
|  |       \/ 62501 *cos|---------||   \/ 62501 *sin|---------|| |  |     \/ 62501 *cos|---------||   \/ 62501 *sin|---------||
|  |  1                 \    2    /|                \    2    /| |  |1                 \    2    /|                \    2    /|
|I*|- -- + ------------------------| + ------------------------|*|I*|-- - ------------------------| + ------------------------|
\  \  25              25           /              25           / \  \25              25           /              25           /
(625014sin⁡(atan⁡(250)2)25+i(−125+625014cos⁡(atan⁡(250)2)25))(625014sin⁡(atan⁡(250)2)25+i(−625014cos⁡(atan⁡(250)2)25+125))\left(\frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{1}{25} + \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25}\right)\right) \left(\frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + \frac{1}{25}\right)\right) 
=
                    4 _______    /atan(250)\
        _______   2*\/ 62501 *cos|---------|
 1    \/ 62501                   \    2    /
--- + --------- - --------------------------
625      625                 625
−2625014cos⁡(atan⁡(250)2)625+1625+62501625- \frac{2 \sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{625} + \frac{1}{625} + \frac{\sqrt{62501}}{625} 
1/625 + sqrt(62501)/625 - 2*62501^(1/4)*cos(atan(250)/2)/625
Respuesta rápida [src] 
       /       4 _______    /atan(250)\\   4 _______    /atan(250)\
       |       \/ 62501 *cos|---------||   \/ 62501 *sin|---------|
       |  1                 \    2    /|                \    2    /
x1 = I*|- -- + ------------------------| + ------------------------
       \  25              25           /              25
x1=625014sin⁡(atan⁡(250)2)25+i(−125+625014cos⁡(atan⁡(250)2)25)x_{1} = \frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{1}{25} + \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25}\right) 
       /     4 _______    /atan(250)\\   4 _______    /atan(250)\
       |     \/ 62501 *cos|---------||   \/ 62501 *sin|---------|
       |1                 \    2    /|                \    2    /
x2 = I*|-- - ------------------------| + ------------------------
       \25              25           /              25
x2=625014sin⁡(atan⁡(250)2)25+i(−625014cos⁡(atan⁡(250)2)25+125)x_{2} = \frac{\sqrt[4]{62501} \sin{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + i \left(- \frac{\sqrt[4]{62501} \cos{\left(\frac{\operatorname{atan}{\left(250 \right)}}{2} \right)}}{25} + \frac{1}{25}\right) 
x2 = 62501^(1/4)*sin(atan(250)/2)/25 + i*(-62501^(1/4)*cos(atan(250)/2)/25 + 1/25)
Respuesta numérica [src] 
x1 = 0.446320064520519 + 0.408108915324835*i
x2 = 0.446320064520519 - 0.408108915324835*i
x2 = 0.446320064520519 - 0.408108915324835*i
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