Hay [matemáticas] 100 [/ matemáticas] raíces o soluciones a la ecuación dada ([matemáticas] 38 x + 8 = x ^ {100} [/ matemáticas]), o para ser precisos complejos [matemáticas] 98 [/ matemáticas] raíces valoradas y dos raíces valoradas reales.
Usando Mathematica y escribiendo el código:
N [Resolver [38 x + 8 == x ^ 100, x], 10]
produce las siguientes cien raíces (lista completa):
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- Cómo demostrar cosx = 2cos ^ 2 (x / 2) -1
- ¿Cuál es la solución de x = sinx / n?
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[matemáticas] \ {x \ a -0.2105263158 \}, \ {x \ a 1.039361309 \}, \\ \ {x \ to -1.0345243702-0.0329248003 i \}, \ {x \ to -1.0345243702 + 0.0329248003 i \}, \\ \ {x \ to -1.0303507192-0.0986417782 i \}, \ {x \ to -1.0303507192 + 0.0986417782 i \}, \\ \ {x \ to -1.0220202069-0.1639614232 i \}, \ {x \ to -1.0220202069 +0.1639614232 i \}, \\ \ {x \ to -1.0095663453-0.2286206301 i \}, \ {x \ to -1.0095663453 + 0.2286206301 i \}, \\ \ {x \ to -0.9930392361-0.2923589604 i \}, \ {x \ to -0.9930392361 + 0.2923589604 i \}, \\ \ {x \ to -0.9725053699-0.3549196942 i \}, \ {x \ to -0.9725053699 + 0.3549196942 i \}, \\ \ {x \ to -0.9480473618- 0.4160508650 i \}, \ {x \ to -0.9480473618 + 0.4160508650 i \}, \\ \ {x \ to -0.9197636205-0.4755062761 i \}, \ {x \ to -0.9197636205 + 0.4755062761 i \}, \\ \ { x \ to -0.8877679558-0.5330464922 i \}, \ {x \ to -0.8877679558 + 0.5330464922 i \}, \\ \ {x \ to -0.8521891223-0.5884398041 i \}, \ {x \ to -0.8521891223 + 0.5884398041 }, \\ \ {x \ to -0.8131703036-0.6414631606 i \}, \ {x \ to -0.8131703036 + 0.6414631606 i \}, \\ \ {x \ to -0.7708685385-0.6919030660 i \}, \ {x \ to -0.7708685385 + 0.6919030660 i \}, \\ \ {x \ to -0.7254540900-0.7395564387 i \}, \ {x \ to -0.7254540900 + 0.7395564387 i \}, \\ \ {x \ to -0.6771097613-0.7842314267 i \}, \ {x \ to -0.6771097613 + 0.7842314267 i \}, \\ \ {x \ to -0.6260301612-0.8257481793 i \}, \ {x \ to -0.6260301612 + 0.8257481793 i \}, \\ \ {x \ to -0.5724209207-0.8639395687 i \}, \ {x \ to -0.5724209207 + 0.8639395687 i \}, \\ \ {x \ to -0.5164978656-0.8986518621 i \}, \ {x \ to -0.5164978656 + 0.8986518621 i \}, \\ \ {x \ to -0.4584861477-0.9297453386 i \}, \ {x \ to -0.4584861477 + 0.9297453386 i \}, \\ \ {x \ to -0.3986193375-0.9570948504 i \}, \ {x \ to -0.3986193375 + 0.9570948504 i \}, \\ \ {x \ a -0.3371384838-0.9805903257 i \}, \ {x \ to -0.3371384838 + 0.9805903257 i \}, \\ \ {x \ to -0.2742911424-1.0001372104 i \}, \ {x \ to -0.2742911424 + 1.0001372104 i \}, \\ \ {x \ to -0.2103303784-1.0156568483 i \}, \ {x \ to -0.2103303784 + 1.0156568483 i \}, \\ \ {x \ to -0.1455137468-1.0270867968 i \}, \ {x \ to -0.1455137468 +1.0270867968 i \}, \\ \ {x \ to -0.0801022545-1.0343810778 i \}, \ {x \ to -0.0801022545 + 1.0343810778 i \}, \\ \ {x \ to -0.0143593085-1.0375103623 i \}, \ {x \ a -0.014 3593085 + 1.0375103623 i \}, \\ \ {x \ to 0.0514503454-1.0364620882 i \}, \ {x \ to 0.0514503454 + 1.0364620882 i \}, \\ \ {x \ to 0.1170616891-1.0312405108 i \}, \ {x \ to 0.1170616891 + 1.0312405108 i \}, \\ \ {x \ to 0.1822105005-1.0218666855 i \}, \ {x \ to 0.1822105005 + 1.0218666855 i \}, \\ \ {x \ to 0.2466344179-1.0083783827 i \}, \ {x \ to 0.2466344179 + 1.0083783827 i \}, \\ \ {x \ to 0.3100739967-0.9908299361 i \}, \ {x \ to 0.3100739967 + 0.9908299361 i \}, \\ \ {x \ to 0.3722737550-0.9692920241 i \} , \ {x \ a 0.3722737550 + 0.9692920241 i \}, \\ \ {x \ to 0.4329832028-0.9438513848 i \}, \ {x \ to 0.4329832028 + 0.9438513848 i \}, \\ \ {x \ to 0.4919578507-0.9146104674 i \}, \ {x \ a 0.4919578507 + 0.9146104674 i \}, \\ \ {x \ a 0.5489601951-0.8816870197 i \}, \ {x \ a 0.5489601951 + 0.8816870197 i \}, \\ \ {x \ a 0.6037606749- 0.8452136140 i \}, \ {x \ a 0.6037606749 + 0.8452136140 i \}, \\ \ {x \ to 0.6561385958-0.8053371138 i \}, \ {x \ to 0.6561385958 + 0.8053371138 i \}, \\ \ {x \ to 0.7058830197-0.7622180825 i \}, \ {x \ a 0.7058830197 + 0.7622180825 i \}, \\ \ {x \ a 0.7527936139-0.7160301372 i \}, \ {x \ a 0.75 27936139 + 0.7160301372 i \}, \\ \ {x \ a 0.7966814581-0.6669592497 i \}, \ {x \ a 0.7966814581 + 0.6669592497 i \}, \\ \ {x \ a 0.8373698052-0.6152029978 i \}, \ {x \ to 0.8373698052 + 0.6152029978 i \}, \\ \ {x \ to 0.8746947936-0.5609697703 i \}, \ {x \ to 0.8746947936 + 0.5609697703 i \}, \\ \ {x \ to 0.9085061064-0.5044779279 i \}, \ {x \ a 0.9085061064 + 0.5044779279 i \}, \\ \ {x \ a 0.9386675771-0.4459549239 i \}, \ {x \ a 0.9386675771 + 0.4459549239 i \}, \\ \ {x \ a 0.9650577385-0.3856363892 i \} , \ {x \ to 0.9650577385 + 0.3856363892 i \}, \\ \ {x \ to 0.9875703107-0.3237651831 i \}, \ {x \ to 0.9875703107 + 0.3237651831 i \}, \\ \ {x \ to 1.0061146305-0.2605904157 i \}, \ {x \ a 1.0061146305 + 0.2605904157 i \}, \\ \ {x \ to 1.0206160153-0.1963664453 i \}, \ {x \ to 1.0206160153 + 0.1963664453 i \}, \\ \ {x \ to 1.0310160646- 0.1313518542 i \}, \ {x \ to 1.0310160646 + 0.1313518542 i \}, \\ \ {x \ to 1.0372728949-0.0658084077 i \}, \ {x \ to 1.0372728949 + 0.0658084077 i \} [/ math]
Se puede notar que las dos primeras raíces en la lista anterior son las que tienen un valor real. Sus valores numéricos son más exactamente iguales a:
[matemáticas] x \ aprox -0.2105263157894736842105263157894736842105 [/ matemáticas]
y
[matemáticas] x \ aprox 1.039361308506519560668078388758894959882 [/ matemáticas]
A continuación se muestra una gráfica de las funciones [matemáticas] 38 x + 8 [/ matemáticas] y [matemáticas] x ^ {100} [/ matemáticas], y de sus puntos de intersección que tienen como abscisas las raíces valoradas reales (de Wolfram Alpha) :
