2t-3t/t+3-t=t-1-2t/10-(t+3) eching

$$\frac { 2 t - 3 t } { t + 3 - t } = \frac { t - 1 - 2 t } { 10 - ( t + 3 ) }$$

t uchun yechish

$$t=1$$

$$t=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

t qiymati 7 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3\left(t-7\right) ga, t+3-t,10-\left(t+3\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(t-7\right)\left(2t-3t\right)=-3\left(t-1-2t\right)$$

-t ni olish uchun 2t va -3t ni birlashtirish.

$$\left(t-7\right)\left(-1\right)t=-3\left(t-1-2t\right)$$

t-7 ga -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-t+7\right)t=-3\left(t-1-2t\right)$$

-t+7 ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-t^{2}+7t=-3\left(t-1-2t\right)$$

-t ni olish uchun t va -2t ni birlashtirish.

$$-t^{2}+7t=-3\left(-t-1\right)$$

-3 ga -t-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-t^{2}+7t=3t+3$$

Ikkala tarafdan 3t ni ayirish.

$$-t^{2}+7t-3t=3$$

4t ni olish uchun 7t va -3t ni birlashtirish.

$$-t^{2}+4t=3$$

Ikkala tarafdan 3 ni ayirish.

$$-t^{2}+4t-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 4 ni b va -3 ni c bilan almashtiring.

$$t=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$t=\frac{-4±\sqrt{16-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$t=\frac{-4±\sqrt{16+4\left(-3\right)}}{2\left(-1\right)}$$

4 ni -3 marotabaga ko'paytirish.

$$t=\frac{-4±\sqrt{16-12}}{2\left(-1\right)}$$

16 ni -12 ga qo'shish.

$$t=\frac{-4±\sqrt{4}}{2\left(-1\right)}$$

4 ning kvadrat ildizini chiqarish.

$$t=\frac{-4±2}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$t=\frac{-4±2}{-2}$$

t=\frac{-4±2}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 2 ga qo'shish.

$$t=-\frac{2}{-2}$$

-2 ni -2 ga bo'lish.

$$t=1$$

t=\frac{-4±2}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 2 ni ayirish.

$$t=-\frac{6}{-2}$$

-6 ni -2 ga bo'lish.

$$t=3$$

Tenglama yechildi.

$$t=1 t=3$$

Kvadratni yakunlash bo'yicha qadamlar

t qiymati 7 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3\left(t-7\right) ga, t+3-t,10-\left(t+3\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(t-7\right)\left(2t-3t\right)=-3\left(t-1-2t\right)$$

-t ni olish uchun 2t va -3t ni birlashtirish.

$$\left(t-7\right)\left(-1\right)t=-3\left(t-1-2t\right)$$

t-7 ga -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-t+7\right)t=-3\left(t-1-2t\right)$$

-t+7 ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-t^{2}+7t=-3\left(t-1-2t\right)$$

-t ni olish uchun t va -2t ni birlashtirish.

$$-t^{2}+7t=-3\left(-t-1\right)$$

-3 ga -t-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-t^{2}+7t=3t+3$$

Ikkala tarafdan 3t ni ayirish.

$$-t^{2}+7t-3t=3$$

4t ni olish uchun 7t va -3t ni birlashtirish.

$$-t^{2}+4t=3$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-t^{2}+4t}{-1}=\frac{3}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$t^{2}+\frac{4}{-1}t=\frac{3}{-1}$$

4 ni -1 ga bo'lish.

$$t^{2}-4t=\frac{3}{-1}$$

3 ni -1 ga bo'lish.

$$t^{2}-4t=-3$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-4t+\left(-2\right)^{2}=-3+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$t^{2}-4t+4=-3+4$$

-3 ni 4 ga qo'shish.

$$t^{2}-4t+4=1$$

t^{2}-4t+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-2\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-2\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$t-2=1 t-2=-1$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$t=3 t=1$$