Datrys {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}

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

Datrys ar gyfer f, x, g, h, j, k, l, m, n, o, p, q, r

$$r=i$$

Camau Ateb

Ystyriwch y pedwaredd hafaliad. Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$h=i$$

Ystyriwch y trydydd hafaliad. Mewnosod y gwerthoedd sy’n hysbys i’r hafaliad.

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

Rhannu’r ddwy ochr â -3.

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

Rhannu i â -3 i gael -\frac{1}{3}i.

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

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

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

Ystyriwch yr hafaliad cyntaf. Mewnosod y gwerthoedd sy’n hysbys i’r hafaliad.

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

Ychwanegu 6x at y ddwy ochr.

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

Cyfuno -\frac{1}{3}ix a 6x i gael \left(6-\frac{1}{3}i\right)x.

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

Rhannu’r ddwy ochr â 6-\frac{1}{3}i.

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

Lluoswch rifiadur ac enwadur \frac{3}{6-\frac{1}{3}i} gyda chyfiau cymhleth yr enwadur 6+\frac{1}{3}i.

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

Gwnewch y gwaith lluosi yn \frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}.

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

Rhannu 18+i â \frac{325}{9} i gael \frac{162}{325}+\frac{9}{325}i.

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

Ystyriwch yr ail hafaliad. Mewnosod y gwerthoedd sy’n hysbys i’r hafaliad.

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

Lluosi 3 a \frac{162}{325}+\frac{9}{325}i i gael \frac{486}{325}+\frac{27}{325}i.

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

Cyfrifo \frac{162}{325}+\frac{9}{325}i i bŵer -3 a chael \frac{214}{27}-\frac{971}{729}i.

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

Lluosi 21 a \frac{214}{27}-\frac{971}{729}i i gael \frac{1498}{9}-\frac{6797}{243}i.

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

Adio \frac{486}{325}+\frac{27}{325}i a \frac{1498}{9}-\frac{6797}{243}i i gael \frac{491224}{2925}-\frac{2202464}{78975}i.

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

Rhannu’r ddwy ochr â \frac{162}{325}+\frac{9}{325}i.

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

Lluoswch rifiadur ac enwadur \frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i} gyda chyfiau cymhleth yr enwadur \frac{162}{325}-\frac{9}{325}i.

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

Gwnewch y gwaith lluosi yn \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)}.

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

Rhannu \frac{55984}{675}-\frac{18088}{975}i â \frac{81}{325} i gael \frac{727792}{2187}-\frac{18088}{243}i.

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

Mae’r system wedi’i datrys nawr.

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