Réitigh {l}{f{(x)}=-6x+3}{g{(x)}=3x+21x^-3}{h=f{(-3)}}{i=h}{j=i}{k=j}{l=k}{m=l}{n=m}{o=n}{p=o}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { f {(x)} = -6 x + 3 }\\ { g {(x)} = 3 x + 21 x ^ {-3} }\\ { h = f {(-3)} }\\ { i = h }\\ { j = i }\\ { k = j }\\ { l = k }\\ { m = l }\\ { n = m }\\ { o = n }\\ { p = o }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

Réitigh do f,x,g,h,j,k,l,m,n,o,p,q,r.

$$r=i$$

Céimeanna Réitigh

Cuir an ceathrú cothromóid san áireamh. Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$h=i$$

Cuir an tríú cothromóid san áireamh. Ionsáigh luachanna aitheanta na n-athróg sa chothromóid.

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

Roinn an dá thaobh faoi -3.

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

Roinn i faoi -3 chun -\frac{1}{3}i a fháil.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Cuir an chéad cothromóid san áireamh. Ionsáigh luachanna aitheanta na n-athróg sa chothromóid.

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

Cuir 6x leis an dá thaobh.

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

Comhcheangail -\frac{1}{3}ix agus 6x chun \left(6-\frac{1}{3}i\right)x a fháil.

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

Roinn an dá thaobh faoi 6-\frac{1}{3}i.

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

Iolraigh uimhreoir agus ainmneoir \frac{3}{6-\frac{1}{3}i} faoi chomhchuingeach coimpléascach an ainmneora, 6+\frac{1}{3}i.

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

Déan iolrúcháin in \frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}.

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

Roinn 18+i faoi \frac{325}{9} chun \frac{162}{325}+\frac{9}{325}i a fháil.

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

Cuir an dara cothromóid san áireamh. Ionsáigh luachanna aitheanta na n-athróg sa chothromóid.

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

Méadaigh 3 agus \frac{162}{325}+\frac{9}{325}i chun \frac{486}{325}+\frac{27}{325}i a fháil.

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

Ríomh cumhacht \frac{162}{325}+\frac{9}{325}i de -3 agus faigh \frac{214}{27}-\frac{971}{729}i.

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

Méadaigh 21 agus \frac{214}{27}-\frac{971}{729}i chun \frac{1498}{9}-\frac{6797}{243}i a fháil.

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

Suimigh \frac{486}{325}+\frac{27}{325}i agus \frac{1498}{9}-\frac{6797}{243}i chun \frac{491224}{2925}-\frac{2202464}{78975}i a fháil.

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

Roinn an dá thaobh faoi \frac{162}{325}+\frac{9}{325}i.

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

Iolraigh uimhreoir agus ainmneoir \frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i} faoi chomhchuingeach coimpléascach an ainmneora, \frac{162}{325}-\frac{9}{325}i.

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

Déan iolrúcháin in \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)}.

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

Roinn \frac{55984}{675}-\frac{18088}{975}i faoi \frac{81}{325} chun \frac{727792}{2187}-\frac{18088}{243}i a fháil.

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

Tá an córas réitithe anois.

$$f=-\frac{1}{3}i x=\frac{162}{325}+\frac{9}{325}i g=\frac{727792}{2187}-\frac{18088}{243}i h=i j=i k=i l=i m=i n=i o=i p=i q=i r=i$$