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

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

m uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

9m-2 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini 9x^{2}-6x+1 ga bo‘ling.

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

9x^{2}-6x+1 ga bo'lish 9x^{2}-6x+1 ga ko'paytirishni bekor qiladi.

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

2x^{2} ni 9x^{2}-6x+1 ga bo'lish.

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

x uchun yechish (complex solution)

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

x uchun yechish

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