3d/frac{d{v_{1}}+d/v_{2}+d/v_{2}}=frac{3v_{1}v_{2}}{2v_{1}+v_{2}} eching

$$\frac { 3 d } { \frac { d } { v _ { 1 } } + \frac { d } { v _ { 2 } } + \frac { d } { v _ { 2 } } } = \frac { 3 v _ { 1 } v _ { 2 } } { 2 v _ { 1 } + v _ { 2 } }$$

d uchun yechish

$$d\neq 0$$

$$v_{1}\neq -\frac{v_{2}}{2}\text{ and }v_{1}\neq 0\text{ and }v_{2}\neq 0$$

Yechim qadamlari

Tenglamaning ikkala tarafini 2v_{1}+v_{2} ga ko'paytirish.

$$d^{-1}v_{1}v_{2}\times 3d=3v_{1}v_{2}$$

Shartlarni qayta saralash.

$$3\times \frac{1}{d}dv_{1}v_{2}=3v_{1}v_{2}$$

3ni ikki tarafidan bekor qilish.

$$\frac{1}{d}dv_{1}v_{2}=v_{1}v_{2}$$

d qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini d ga ko'paytirish.

$$1dv_{1}v_{2}=v_{1}v_{2}d$$

Ikkala tarafdan v_{1}v_{2}d ni ayirish.

$$1dv_{1}v_{2}-v_{1}v_{2}d=0$$

0 ni olish uchun 1dv_{1}v_{2} va -v_{1}v_{2}d ni birlashtirish.

$$0=0$$

0 va 0 ni taqqoslang.

$$\text{true}$$

Bu har qanday d uchun to‘g‘ri.

$$d\in \mathrm{R}$$

d qiymati 0 teng bo‘lmaydi.

$$d\in \mathrm{R}\setminus 0$$

v_1 uchun yechish (complex solution)

$$v_{1}\in \mathrm{C}\setminus -\frac{v_{2}}{2},0$$

$$d\neq 0\text{ and }v_{2}\neq 0$$

v_1 uchun yechish

$$v_{1}\in \mathrm{R}\setminus -\frac{v_{2}}{2},0$$

$$d\neq 0\text{ and }v_{2}\neq 0$$