Réitigh 12=(1-3x)(1-3x)d+(1+3x)(1+3x)

$$12 = ( 1 - 3 x ) ( 1 - 3 x ) d + ( 1 + 3 x ) ( 1 + 3 x )$$

Réitigh do d.

$$d=-\frac{9x^{2}+6x-11}{\left(1-3x\right)^{2}}$$

$$x\neq \frac{1}{3}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh 1-3x agus 1-3x chun \left(1-3x\right)^{2} a fháil.

$$12=\left(1-3x\right)^{2}d+\left(1+3x\right)\left(1+3x\right)$$

Méadaigh 1+3x agus 1+3x chun \left(1+3x\right)^{2} a fháil.

$$12=\left(1-3x\right)^{2}d+\left(1+3x\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(1-3x\right)^{2} a leathnú.

$$12=\left(1-6x+9x^{2}\right)d+\left(1+3x\right)^{2}$$

Úsáid an t-airí dáileach chun 1-6x+9x^{2} a mhéadú faoi d.

$$12=d-6xd+9x^{2}d+\left(1+3x\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(1+3x\right)^{2} a leathnú.

$$12=d-6xd+9x^{2}d+1+6x+9x^{2}$$

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

$$d-6xd+9x^{2}d+1+6x+9x^{2}=12$$

Bain 1 ón dá thaobh.

$$d-6xd+9x^{2}d+6x+9x^{2}=12-1$$

Dealaigh 1 ó 12 chun 11 a fháil.

$$d-6xd+9x^{2}d+6x+9x^{2}=11$$

Bain 6x ón dá thaobh.

$$d-6xd+9x^{2}d+9x^{2}=11-6x$$

Bain 9x^{2} ón dá thaobh.

$$d-6xd+9x^{2}d=11-6x-9x^{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil d.

$$\left(1-6x+9x^{2}\right)d=11-6x-9x^{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(9x^{2}-6x+1\right)d=11-6x-9x^{2}$$

Roinn an dá thaobh faoi 1-6x+9x^{2}.

$$\frac{\left(9x^{2}-6x+1\right)d}{9x^{2}-6x+1}=\frac{11-6x-9x^{2}}{9x^{2}-6x+1}$$

Má roinntear é faoi 1-6x+9x^{2} cuirtear an iolrúchán faoi 1-6x+9x^{2} ar ceal.

$$d=\frac{11-6x-9x^{2}}{9x^{2}-6x+1}$$

Roinn 11-6x-9x^{2} faoi 1-6x+9x^{2}.

$$d=\frac{11-6x-9x^{2}}{\left(3x-1\right)^{2}}$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}x=-\frac{-d+2\sqrt{2d+3}+1}{3\left(d+1\right)}\text{; }x=-\frac{-d-2\sqrt{2d+3}+1}{3\left(d+1\right)}\text{, }&d\neq -1\\x=1\text{, }&d=-1\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}x=-\frac{-d+2\sqrt{2d+3}+1}{3\left(d+1\right)}\text{; }x=-\frac{-d-2\sqrt{2d+3}+1}{3\left(d+1\right)}\text{, }&d\neq -1\text{ and }d\geq -\frac{3}{2}\\x=1\text{, }&d=-1\end{matrix}\right.$$