Réitigh (9m-2)x^2-6mx+m=0

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

Réitigh do m.

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

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun 9m-2 a mhéadú faoi x^{2}.

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

Cuir 2x^{2} leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

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

Comhcheangail na téarmaí ar fad ina bhfuil m.

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

Roinn an dá thaobh faoi 9x^{2}-6x+1.

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

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

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

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

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

Réitigh do x. (complex solution)

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

Réitigh do x.

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