Datrys (k-1)x^2+3kx+2k-3=0

$$( k - 1 ) x ^ { 2 } + 3 k x + 2 k - 3 = 0$$

Datrys ar gyfer k

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

$$x\neq -2\text{ and }x\neq -1$$

Camau ar gyfer Datrys Hafaliad Llinol

Defnyddio’r briodwedd ddosbarthu i luosi k-1 â x^{2}.

$$kx^{2}-x^{2}+3kx+2k-3=0$$

Ychwanegu x^{2} at y ddwy ochr. Mae adio unrhyw beth at sero yn cyrraedd ei swm ei hun.

$$kx^{2}+3kx+2k-3=x^{2}$$

Ychwanegu 3 at y ddwy ochr.

$$kx^{2}+3kx+2k=x^{2}+3$$

Cyfuno pob term sy'n cynnwys k.

$$\left(x^{2}+3x+2\right)k=x^{2}+3$$

Rhannu’r ddwy ochr â x^{2}+3x+2.

$$\frac{\left(x^{2}+3x+2\right)k}{x^{2}+3x+2}=\frac{x^{2}+3}{x^{2}+3x+2}$$

Mae rhannu â x^{2}+3x+2 yn dad-wneud lluosi â x^{2}+3x+2.

$$k=\frac{x^{2}+3}{x^{2}+3x+2}$$

Rhannwch x^{2}+3 â x^{2}+3x+2.

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

Datrys ar gyfer x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\neq 1\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right.$$

Datrys ar gyfer x

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\leq -4\sqrt{7}-10\text{ or }\left(k\neq 1\text{ and }k\geq 4\sqrt{7}-10\right)\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right.$$