Réitigh {l}{f{(x)}=20{(2x^3+3x^2-2x)}}{g=8x}{h=g}{i=h}{j=i}{k=j}{l=k}{text{Solvefor}mtext{where}}{m=l}

$$\left. \begin{array} { l } { f {(x)} = 20 {(2 x ^ {3} + 3 x ^ {2} - 2 x)} }\\ { g = 8 x }\\ { h = g }\\ { i = h }\\ { j = i }\\ { k = j }\\ { l = k }\\ { \text{Solve for } m \text{ where} } \\ { m = l } \end{array} \right.$$

Réitigh do f,x,g,h,j,k,l,m.

$$m=i$$

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.

$$i=g$$

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

$$g=i$$

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

$$i=8x$$

Roinn an dá thaobh faoi 8.

$$\frac{i}{8}=x$$

Roinn i faoi 8 chun \frac{1}{8}i a fháil.

$$\frac{1}{8}i=x$$

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

$$x=\frac{1}{8}i$$

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

$$f\times \left(\frac{1}{8}i\right)=20\left(2\times \left(\frac{1}{8}i\right)^{3}+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Ríomh cumhacht \frac{1}{8}i de 3 agus faigh -\frac{1}{512}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(2\times \left(-\frac{1}{512}i\right)+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Méadaigh 2 agus -\frac{1}{512}i chun -\frac{1}{256}i a fháil.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Ríomh cumhacht \frac{1}{8}i de 2 agus faigh -\frac{1}{64}.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i+3\left(-\frac{1}{64}\right)-2\times \left(\frac{1}{8}i\right)\right)$$

Méadaigh 3 agus -\frac{1}{64} chun -\frac{3}{64} a fháil.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i-\frac{3}{64}-2\times \left(\frac{1}{8}i\right)\right)$$

Méadaigh -2 agus \frac{1}{8}i chun -\frac{1}{4}i a fháil.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i-\frac{3}{64}-\frac{1}{4}i\right)$$

Déan suimiú in -\frac{1}{256}i-\frac{3}{64}-\frac{1}{4}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{3}{64}-\frac{65}{256}i\right)$$

Méadaigh 20 agus -\frac{3}{64}-\frac{65}{256}i chun -\frac{15}{16}-\frac{325}{64}i a fháil.

$$f\times \left(\frac{1}{8}i\right)=-\frac{15}{16}-\frac{325}{64}i$$

Roinn an dá thaobh faoi \frac{1}{8}i.

$$f=\frac{-\frac{15}{16}-\frac{325}{64}i}{\frac{1}{8}i}$$

Iolraigh uimhreoir agus ainmneoir \frac{-\frac{15}{16}-\frac{325}{64}i}{\frac{1}{8}i} faoin aonad samhailteach i.

$$f=\frac{\frac{325}{64}-\frac{15}{16}i}{-\frac{1}{8}}$$

Roinn \frac{325}{64}-\frac{15}{16}i faoi -\frac{1}{8} chun -\frac{325}{8}+\frac{15}{2}i a fháil.

$$f=-\frac{325}{8}+\frac{15}{2}i$$

Tá an córas réitithe anois.

$$f=-\frac{325}{8}+\frac{15}{2}i x=\frac{1}{8}i g=i h=i j=i k=i l=i m=i$$