Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((x^2+1/(x^2))^2+10*(x+1/x)^2+5)
¿Cómo vas a descomponer esta sqrt((x^2+1/(x^2))^2+10*(x+1/x)^2+5) expresión en fracciones?
Solución
Ha introducido
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/ 2 2
/ / 2 1 \ / 1\
/ |x + --| + 10*|x + -| + 5
/ | 2| \ x/
\/ \ x /
$$\sqrt{\left(10 \left(x + \frac{1}{x}\right)^{2} + \left(x^{2} + \frac{1}{x^{2}}\right)^{2}\right) + 5}$$
sqrt((x^2 + 1/(x^2))^2 + 10*(x + 1/x)^2 + 5)
Descomposición de una fracción
[src]
sqrt(25 + x^(-4) + x^4 + 10/x^2 + 10*x^2 + 2*x^2/x^2)
$$\sqrt{x^{4} + \frac{2 x^{2}}{x^{2}} + 10 x^{2} + 25 + \frac{10}{x^{2}} + \frac{1}{x^{4}}}$$
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/ 2
/ 1 4 10 2 2*x
/ 25 + -- + x + -- + 10*x + ----
/ 4 2 2
\/ x x x
Simplificación general
[src]
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/ 1 4 10 2
/ 27 + -- + x + -- + 10*x
/ 4 2
\/ x x
$$\sqrt{x^{4} + 10 x^{2} + 27 + \frac{10}{x^{2}} + \frac{1}{x^{4}}}$$
sqrt(27 + x^(-4) + x^4 + 10/x^2 + 10*x^2)
Denominador común
[src]
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/ 1 4 10 2
/ 27 + -- + x + -- + 10*x
/ 4 2
\/ x x
$$\sqrt{x^{4} + 10 x^{2} + 27 + \frac{10}{x^{2}} + \frac{1}{x^{4}}}$$
sqrt(27 + x^(-4) + x^4 + 10/x^2 + 10*x^2)
Compilar la expresión
[src]
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/ 2 2
/ /1 2\ / 1\
/ 5 + |-- + x | + 10*|x + -|
/ | 2 | \ x/
\/ \x /
$$\sqrt{10 \left(x + \frac{1}{x}\right)^{2} + \left(x^{2} + \frac{1}{x^{2}}\right)^{2} + 5}$$
sqrt(5 + (x^(-2) + x^2)^2 + 10*(x + 1/x)^2)
Combinatoria
[src]
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/ 1 4 10 2
/ 27 + -- + x + -- + 10*x
/ 4 2
\/ x x
$$\sqrt{x^{4} + 10 x^{2} + 27 + \frac{10}{x^{2}} + \frac{1}{x^{4}}}$$
sqrt(27 + x^(-4) + x^4 + 10/x^2 + 10*x^2)
Potencias
[src]
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/ 2 2
/ /1 2\ / 1\
/ 5 + |-- + x | + 10*|x + -|
/ | 2 | \ x/
\/ \x /
$$\sqrt{10 \left(x + \frac{1}{x}\right)^{2} + \left(x^{2} + \frac{1}{x^{2}}\right)^{2} + 5}$$
sqrt(5 + (x^(-2) + x^2)^2 + 10*(x + 1/x)^2)
Parte trigonométrica
[src]
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/ 2 2
/ /1 2\ / 1\
/ 5 + |-- + x | + 10*|x + -|
/ | 2 | \ x/
\/ \x /
$$\sqrt{10 \left(x + \frac{1}{x}\right)^{2} + \left(x^{2} + \frac{1}{x^{2}}\right)^{2} + 5}$$
sqrt(5 + (x^(-2) + x^2)^2 + 10*(x + 1/x)^2)
Denominador racional
[src]
______________________________
/ 2 2
/ /1 2\ / 1\
/ 5 + |-- + x | + 10*|x + -|
/ | 2 | \ x/
\/ \x /
$$\sqrt{10 \left(x + \frac{1}{x}\right)^{2} + \left(x^{2} + \frac{1}{x^{2}}\right)^{2} + 5}$$
sqrt(5 + (x^(-2) + x^2)^2 + 10*(x + 1/x)^2)
Unión de expresiones racionales
[src]
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/ 2 2
/ / 4\ 4 2 / 2\
/ \1 + x / + 5*x + 10*x *\1 + x /
/ ----------------------------------
/ 4
\/ x
$$\sqrt{\frac{5 x^{4} + 10 x^{2} \left(x^{2} + 1\right)^{2} + \left(x^{4} + 1\right)^{2}}{x^{4}}}$$
sqrt(((1 + x^4)^2 + 5*x^4 + 10*x^2*(1 + x^2)^2)/x^4)
Respuesta numérica
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3.16227766016838*(0.5 + (x + 1/x)^2 + 0.1*(x^(-2) + x^2)^2)^0.5
3.16227766016838*(0.5 + (x + 1/x)^2 + 0.1*(x^(-2) + x^2)^2)^0.5