2m/3n^2=4t^2/5w eching

$$\frac { 2 m } { 3 n ^ { 2 } } = \frac { 4 t ^ { 2 } } { 5 w }$$

m uchun yechish

$$m=\frac{6\left(nt\right)^{2}}{5w}$$

$$n\neq 0\text{ and }w\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 15wn^{2} ga, 3n^{2},5w ning eng kichik karralisiga ko‘paytiring.

$$5w\times 2m=3n^{2}\times 4t^{2}$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$10wm=3n^{2}\times 4t^{2}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$10wm=12n^{2}t^{2}$$

Ikki tarafini 10w ga bo‘ling.

$$\frac{10wm}{10w}=\frac{12n^{2}t^{2}}{10w}$$

10w ga bo'lish 10w ga ko'paytirishni bekor qiladi.

$$m=\frac{12n^{2}t^{2}}{10w}$$

12n^{2}t^{2} ni 10w ga bo'lish.

$$m=\frac{6n^{2}t^{2}}{5w}$$

n uchun yechish

$$\left\{\begin{matrix}n=\frac{\sqrt{30mw}}{6t}\text{; }n=-\frac{\sqrt{30mw}}{6t}\text{, }&\left(t\neq 0\text{ and }w<0\text{ and }m<0\right)\text{ or }\left(t\neq 0\text{ and }m>0\text{ and }w>0\right)\\n\neq 0\text{, }&t=0\text{ and }m=0\text{ and }w\neq 0\end{matrix}\right,$$