2sqrt{4(t-1)}=sqrt{4(2t-1)} eching

$$2 \sqrt { 4 ( t - 1 ) } = \sqrt { 4 ( 2 t - 1 ) }$$

t uchun yechish

$$t = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

\left(2\sqrt{4t-4}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

2 daraja ko‘rsatkichini \sqrt{4t-4} ga hisoblang va 4t-4 ni qiymatni oling.

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

4 ga 4t-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

4 ga 2t-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16t-16=\left(\sqrt{8t-4}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{8t-4} ga hisoblang va 8t-4 ni qiymatni oling.

$$16t-16=8t-4$$

Ikkala tarafdan 8t ni ayirish.

$$16t-16-8t=-4$$

8t ni olish uchun 16t va -8t ni birlashtirish.

$$8t-16=-4$$

16 ni ikki tarafga qo’shing.

$$8t=-4+16$$

12 olish uchun -4 va 16'ni qo'shing.

$$8t=12$$

Ikki tarafini 8 ga bo‘ling.

$$t=\frac{12}{8}$$

\frac{12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t=\frac{3}{2}$$

2\sqrt{4\left(t-1\right)}=\sqrt{4\left(2t-1\right)} tenglamasida t uchun \frac{3}{2} ni almashtiring.

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

Qisqartirish. t=\frac{3}{2} tenglamani qoniqtiradi.

$$2\times 2^{\frac{1}{2}}=2\times 2^{\frac{1}{2}}$$

2\sqrt{4\left(t-1\right)}=\sqrt{4\left(2t-1\right)} tenglamasi noyob yechimga ega.

$$t=\frac{3}{2}$$