Resolver {l}{f{(x)}=-6x+3}{g{(x)}=3x+21x^-3}{h=f{(-3)}}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { f {(x)} = -6 x + 3 }\\ { g {(x)} = 3 x + 21 x ^ {-3} }\\ { h = f {(-3)} }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Resolver f, x, g, h

$$x=\frac{162}{325}+\frac{9}{325}i\approx 0.498461538+0.027692308i$$

$$f=-\frac{1}{3}i\approx -0.333333333i$$

$$g=\frac{727792}{2187}-\frac{18088}{243}i\approx 332.780978509-74.436213992i$$

$$h=i$$

Pasos da solución

Ten en conta a cuarta ecuación. Cambia de lado para que todos os termos variables estean no lado esquerdo.

$$h=i$$

Ten en conta a terceira ecuación. Insire os valores coñecidos das variables na ecuación.

$$i=f\left(-3\right)$$

Divide ambos lados entre -3.

$$\frac{i}{-3}=f$$

Divide i entre -3 para obter -\frac{1}{3}i.

$$-\frac{1}{3}i=f$$

Cambia de lado para que todos os termos variables estean no lado esquerdo.

$$f=-\frac{1}{3}i$$

Ten en conta a primeira ecuación. Insire os valores coñecidos das variables na ecuación.

$$-\frac{1}{3}ix=-6x+3$$

Engadir 6x en ambos lados.

$$-\frac{1}{3}ix+6x=3$$

Combina -\frac{1}{3}ix e 6x para obter \left(6-\frac{1}{3}i\right)x.

$$\left(6-\frac{1}{3}i\right)x=3$$

Divide ambos lados entre 6-\frac{1}{3}i.

$$x=\frac{3}{6-\frac{1}{3}i}$$

Multiplica o numerador e o denominador de \frac{3}{6-\frac{1}{3}i} polo conxugado complexo do denominador, 6+\frac{1}{3}i.

$$x=\frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}$$

Fai as multiplicacións en \frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}.

$$x=\frac{18+i}{\frac{325}{9}}$$

Divide 18+i entre \frac{325}{9} para obter \frac{162}{325}+\frac{9}{325}i.

$$x=\frac{162}{325}+\frac{9}{325}i$$

Ten en conta a segunda ecuación. Insire os valores coñecidos das variables na ecuación.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=3\left(\frac{162}{325}+\frac{9}{325}i\right)+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Multiplica 3 e \frac{162}{325}+\frac{9}{325}i para obter \frac{486}{325}+\frac{27}{325}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Calcula \frac{162}{325}+\frac{9}{325}i á potencia de -3 e obtén \frac{214}{27}-\frac{971}{729}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{214}{27}-\frac{971}{729}i\right)$$

Multiplica 21 e \frac{214}{27}-\frac{971}{729}i para obter \frac{1498}{9}-\frac{6797}{243}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+\left(\frac{1498}{9}-\frac{6797}{243}i\right)$$

Suma \frac{486}{325}+\frac{27}{325}i e \frac{1498}{9}-\frac{6797}{243}i para obter \frac{491224}{2925}-\frac{2202464}{78975}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{491224}{2925}-\frac{2202464}{78975}i$$

Divide ambos lados entre \frac{162}{325}+\frac{9}{325}i.

$$g=\frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i}$$

Multiplica o numerador e o denominador de \frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i} polo conxugado complexo do denominador, \frac{162}{325}-\frac{9}{325}i.

$$g=\frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}$$

Fai as multiplicacións en \frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}.

$$g=\frac{\frac{55984}{675}-\frac{18088}{975}i}{\frac{81}{325}}$$

Divide \frac{55984}{675}-\frac{18088}{975}i entre \frac{81}{325} para obter \frac{727792}{2187}-\frac{18088}{243}i.

$$g=\frac{727792}{2187}-\frac{18088}{243}i$$

O sistema xa funciona correctamente.

$$f=-\frac{1}{3}i x=\frac{162}{325}+\frac{9}{325}i g=\frac{727792}{2187}-\frac{18088}{243}i h=i$$