Datrys 2an+n(n-1)/2x(-3)=70

$$2 a n + \frac { n ( n - 1 ) } { 2 } x ( - 3 ) = 70$$

Datrys ar gyfer a

$$a=\frac{3nx}{4}-\frac{3x}{4}+\frac{35}{n}$$

$$n\neq 0$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluoswch ddwy ochr yr hafaliad â 2.

$$4an+n\left(n-1\right)x\left(-3\right)=140$$

Defnyddio’r briodwedd ddosbarthu i luosi n â n-1.

$$4an+\left(n^{2}-n\right)x\left(-3\right)=140$$

Defnyddio’r briodwedd ddosbarthu i luosi n^{2}-n â x.

$$4an+\left(n^{2}x-nx\right)\left(-3\right)=140$$

Defnyddio’r briodwedd ddosbarthu i luosi n^{2}x-nx â -3.

$$4an-3n^{2}x+3nx=140$$

Ychwanegu 3n^{2}x at y ddwy ochr.

$$4an+3nx=140+3n^{2}x$$

Tynnu 3nx o'r ddwy ochr.

$$4an=140+3n^{2}x-3nx$$

Mae'r hafaliad yn y ffurf safonol.

$$4na=3xn^{2}-3nx+140$$

Rhannu’r ddwy ochr â 4n.

$$\frac{4na}{4n}=\frac{3xn^{2}-3nx+140}{4n}$$

Mae rhannu â 4n yn dad-wneud lluosi â 4n.

$$a=\frac{3xn^{2}-3nx+140}{4n}$$

Rhannwch 140+3n^{2}x-3nx â 4n.

$$a=\frac{3nx}{4}-\frac{3x}{4}+\frac{35}{n}$$

Datrys ar gyfer n (complex solution)

$$\left\{\begin{matrix}n=-\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}-3x-4a}{6x}\text{; }n=\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}+3x+4a}{6x}\text{, }&x\neq 0\\n=\frac{35}{a}\text{, }&x=0\text{ and }a\neq 0\end{matrix}\right.$$

Datrys ar gyfer n

$$\left\{\begin{matrix}n=-\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}-3x-4a}{6x}\text{; }n=\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}+3x+4a}{6x}\text{, }&\left(x\neq 0\text{ and }a\geq -\frac{3x}{4}+\sqrt{105x}\right)\text{ or }\left(x\neq 0\text{ and }a\leq -\frac{3x}{4}-\sqrt{105x}\right)\text{ or }x<0\\n=\frac{35}{a}\text{, }&x=0\text{ and }a\neq 0\end{matrix}\right.$$