Atrisiniet (9m-2)x^2-6mx+m=0

$$( 9 m - 2 ) x ^ { 2 } - 6 m x + m = 0$$

Atrast m

$$m=2\times \left(\frac{x}{3x-1}\right)^{2}$$

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

Lineāra vienādojuma risināšanas darbības

Izmantojiet distributīvo īpašību, lai reizinātu 9m-2 ar x^{2}.

$$9mx^{2}-2x^{2}-6mx+m=0$$

Pievienot 2x^{2} abās pusēs. Jebkuram skaitlim pieskaitot nulli, iegūst to pašu skaitli.

$$9mx^{2}-6mx+m=2x^{2}$$

Savelciet visus locekļus, kuros ir m.

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

Daliet abas puses ar 9x^{2}-6x+1.

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

Dalīšana ar 9x^{2}-6x+1 atsauc reizināšanu ar 9x^{2}-6x+1.

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

Daliet 2x^{2} ar 9x^{2}-6x+1.

$$m=\frac{2x^{2}}{\left(3x-1\right)^{2}}$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{m}\left(3\sqrt{m}+\sqrt{2}\right)}{9m-2}\text{; }x=\frac{\sqrt{m}\left(3\sqrt{m}-\sqrt{2}\right)}{9m-2}\text{, }&m\neq \frac{2}{9}\\x=\frac{1}{6}\text{, }&m=\frac{2}{9}\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt{m}\left(3\sqrt{m}+\sqrt{2}\right)}{9m-2}\text{; }x=\frac{\sqrt{m}\left(3\sqrt{m}-\sqrt{2}\right)}{9m-2}\text{, }&m\neq \frac{2}{9}\text{ and }m\geq 0\\x=\frac{1}{6}\text{, }&m=\frac{2}{9}\end{matrix}\right,$$