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

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

Datrys ar gyfer d

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

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

Camau ar gyfer Datrys Hafaliad Llinol

Lluosi 1-3x a 1-3x i gael \left(1-3x\right)^{2}.

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

Lluosi 1+3x a 1+3x i gael \left(1+3x\right)^{2}.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(1-3x\right)^{2}.

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

Defnyddio’r briodwedd ddosbarthu i luosi 1-6x+9x^{2} â d.

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

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(1+3x\right)^{2}.

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

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

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

Tynnu 1 o'r ddwy ochr.

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

Tynnu 1 o 12 i gael 11.

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

Tynnu 6x o'r ddwy ochr.

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

Tynnu 9x^{2} o'r ddwy ochr.

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

Cyfuno pob term sy'n cynnwys d.

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

Mae'r hafaliad yn y ffurf safonol.

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

Rhannu’r ddwy ochr â 1-6x+9x^{2}.

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

Mae rhannu â 1-6x+9x^{2} yn dad-wneud lluosi â 1-6x+9x^{2}.

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

Rhannwch 11-6x-9x^{2} â 1-6x+9x^{2}.

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

Datrys ar gyfer x (complex solution)

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

Datrys ar gyfer x

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