fm^2-14m-15=0 eching

$$f m ^ { 2 } - 14 m - 15 = 0$$

f uchun yechish

$$f=\frac{14m+15}{m^{2}}$$

$$m\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

14m ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$fm^{2}-15=14m$$

15 ni ikki tarafga qo’shing.

$$fm^{2}=14m+15$$

Tenglama standart shaklda.

$$m^{2}f=14m+15$$

Ikki tarafini m^{2} ga bo‘ling.

$$\frac{m^{2}f}{m^{2}}=\frac{14m+15}{m^{2}}$$

m^{2} ga bo'lish m^{2} ga ko'paytirishni bekor qiladi.

$$f=\frac{14m+15}{m^{2}}$$

m uchun yechish (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{15f+49}+7}{f}\text{; }m=\frac{-\sqrt{15f+49}+7}{f}\text{, }&f\neq 0\\m=-\frac{15}{14}\text{, }&f=0\end{matrix}\right,$$

m uchun yechish

$$\left\{\begin{matrix}m=\frac{\sqrt{15f+49}+7}{f}\text{; }m=\frac{-\sqrt{15f+49}+7}{f}\text{, }&f\neq 0\text{ and }f\geq -\frac{49}{15}\\m=-\frac{15}{14}\text{, }&f=0\end{matrix}\right,$$