4sqrt{a}=sqrt{4a+27} eching

$$4 \sqrt{ a } = \sqrt{ 4a+27 }$$

a uchun yechish

$$a = \frac{9}{4} = 2\frac{1}{4} = 2,25$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(4\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

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

$$4^{2}\left(\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16\left(\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

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

$$16a=\left(\sqrt{4a+27}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{4a+27} ga hisoblang va 4a+27 ni qiymatni oling.

$$16a=4a+27$$

Ikkala tarafdan 4a ni ayirish.

$$16a-4a=27$$

12a ni olish uchun 16a va -4a ni birlashtirish.

$$12a=27$$

Ikki tarafini 12 ga bo‘ling.

$$a=\frac{27}{12}$$

\frac{27}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a=\frac{9}{4}$$

4\sqrt{a}=\sqrt{4a+27} tenglamasida a uchun \frac{9}{4} ni almashtiring.

$$4\sqrt{\frac{9}{4}}=\sqrt{4\times \frac{9}{4}+27}$$

Qisqartirish. a=\frac{9}{4} tenglamani qoniqtiradi.

$$6=6$$

4\sqrt{a}=\sqrt{4a+27} tenglamasi noyob yechimga ega.

$$a=\frac{9}{4}$$