z^2+3t/2=t+7/4 eching

$$\frac { z ^ { 2 } + 3 t } { 2 } = \frac { t + 7 } { 4 }$$

t uchun yechish

$$t=\frac{7-2z^{2}}{5}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga, 2,4 ning eng kichik karralisiga ko‘paytiring.

$$2\left(z^{2}+3t\right)=t+7$$

2 ga z^{2}+3t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2z^{2}+6t=t+7$$

Ikkala tarafdan t ni ayirish.

$$2z^{2}+6t-t=7$$

5t ni olish uchun 6t va -t ni birlashtirish.

$$2z^{2}+5t=7$$

Ikkala tarafdan 2z^{2} ni ayirish.

$$5t=7-2z^{2}$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5t}{5}=\frac{7-2z^{2}}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$t=\frac{7-2z^{2}}{5}$$

z uchun yechish (complex solution)

$$z=-\frac{\sqrt{14-10t}}{2}$$

$$z=\frac{\sqrt{14-10t}}{2}$$

z uchun yechish

$$z=\frac{\sqrt{14-10t}}{2}$$

$$z=-\frac{\sqrt{14-10t}}{2}\text{, }t\leq \frac{7}{5}$$