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absolute((x-sqrt(2))*(x-sqrt(3)))=0,025 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
|/      ___\ /      ___\|       
|\x - \/ 2 /*\x - \/ 3 /| = 1/40
∣(x−2)(x−3)∣=140\left|{\left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right)}\right| = \frac{1}{40}
Simplificar
Solución detallada
Para cada expresión dentro del módulo en la ecuación
admitimos los casos cuando la expresión correspondiente es ">= 0" o "< 0",
resolvemos las ecuaciones obtenidas.

1.
(x−2)(x−3)≥0\left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) \geq 0
o
(x≤−5−262+22+32∧−∞<x)∨(5−262+22+32≤x∧x<∞)\left(x \leq - \frac{\sqrt{5 - 2 \sqrt{6}}}{2} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} \wedge -\infty < x\right) \vee \left(\frac{\sqrt{5 - 2 \sqrt{6}}}{2} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} \leq x \wedge x < \infty\right)
obtenemos la ecuación
(x−2)(x−3)−140=0\left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) - \frac{1}{40} = 0
simplificamos, obtenemos
(x−2)(x−3)−140=0\left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) - \frac{1}{40} = 0
la resolución en este intervalo:
x1=−510−200620+22+32x_{1} = - \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
x2=510−200620+22+32x_{2} = \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}

2.
(x−2)(x−3)<0\left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) < 0
o
x<5−262+22+32∧−5−262+22+32<xx < \frac{\sqrt{5 - 2 \sqrt{6}}}{2} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} \wedge - \frac{\sqrt{5 - 2 \sqrt{6}}}{2} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} < x
obtenemos la ecuación
−(x−2)(x−3)−140=0- \left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) - \frac{1}{40} = 0
simplificamos, obtenemos
−(x−2)(x−3)−140=0- \left(x - \sqrt{2}\right) \left(x - \sqrt{3}\right) - \frac{1}{40} = 0
la resolución en este intervalo:
x3=−490−200620+22+32x_{3} = - \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
x4=490−200620+22+32x_{4} = \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}


Entonces la respuesta definitiva es:
x1=−510−200620+22+32x_{1} = - \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
x2=510−200620+22+32x_{2} = \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
x3=−490−200620+22+32x_{3} = - \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
x4=490−200620+22+32x_{4} = \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}
Gráfica
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.50200
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                   _________________                      _________________                      _________________                      _________________
  ___     ___     /             ___      ___     ___     /             ___      ___     ___     /             ___      ___     ___     /             ___ 
\/ 2    \/ 3    \/  490 - 200*\/ 6     \/ 2    \/ 3    \/  490 - 200*\/ 6     \/ 2    \/ 3    \/  510 - 200*\/ 6     \/ 2    \/ 3    \/  510 - 200*\/ 6  
----- + ----- - -------------------- + ----- + ----- + -------------------- + ----- + ----- - -------------------- + ----- + ----- + --------------------
  2       2              20              2       2              20              2       2              20              2       2              20
(510−200620+22+32)+((−510−200620+22+32)+((−490−200620+22+32)+(490−200620+22+32)))\left(\frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) + \left(\left(- \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) + \left(\left(- \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) + \left(\frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right)\right)\right) 
=
    ___       ___
2*\/ 2  + 2*\/ 3
22+232 \sqrt{2} + 2 \sqrt{3} 
producto
/                   _________________\ /                   _________________\ /                   _________________\ /                   _________________\
|  ___     ___     /             ___ | |  ___     ___     /             ___ | |  ___     ___     /             ___ | |  ___     ___     /             ___ |
|\/ 2    \/ 3    \/  490 - 200*\/ 6  | |\/ 2    \/ 3    \/  490 - 200*\/ 6  | |\/ 2    \/ 3    \/  510 - 200*\/ 6  | |\/ 2    \/ 3    \/  510 - 200*\/ 6  |
|----- + ----- - --------------------|*|----- + ----- + --------------------|*|----- + ----- - --------------------|*|----- + ----- + --------------------|
\  2       2              20         / \  2       2              20         / \  2       2              20         / \  2       2              20         /
(−490−200620+22+32)(490−200620+22+32)(−510−200620+22+32)(510−200620+22+32)\left(- \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) \left(- \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}\right) 
=
9599
----
1600
95991600\frac{9599}{1600} 
9599/1600
Respuesta rápida [src] 
                        _________________
       ___     ___     /             ___ 
     \/ 2    \/ 3    \/  490 - 200*\/ 6  
x1 = ----- + ----- - --------------------
       2       2              20
x1=−490−200620+22+32x_{1} = - \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} 
                        _________________
       ___     ___     /             ___ 
     \/ 2    \/ 3    \/  490 - 200*\/ 6  
x2 = ----- + ----- + --------------------
       2       2              20
x2=490−200620+22+32x_{2} = \frac{\sqrt{490 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} 
                        _________________
       ___     ___     /             ___ 
     \/ 2    \/ 3    \/  510 - 200*\/ 6  
x3 = ----- + ----- - --------------------
       2       2              20
x3=−510−200620+22+32x_{3} = - \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} 
                        _________________
       ___     ___     /             ___ 
     \/ 2    \/ 3    \/  510 - 200*\/ 6  
x4 = ----- + ----- + --------------------
       2       2              20
x4=510−200620+22+32x_{4} = \frac{\sqrt{510 - 200 \sqrt{6}}}{20} + \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} 
x4 = sqrt(510 - 200*sqrt(6))/20 + sqrt(2)/2 + sqrt(3)/2
Respuesta numérica [src] 
x1 = 1.79730874174803
x2 = 1.34895562819394
x2 = 1.34895562819394
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