sqrt{y+3}=sqrt{y}+sqrt{3} eching

$$\sqrt{ y+3 } = \sqrt{ y } + \sqrt{ 3 }$$

y uchun yechish

$$y=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{y+3}\right)^{2}=\left(\sqrt{y}+\sqrt{3}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{y+3} ga hisoblang va y+3 ni qiymatni oling.

$$y+3=\left(\sqrt{y}+\sqrt{3}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\sqrt{y}+\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$y+3=\left(\sqrt{y}\right)^{2}+2\sqrt{y}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

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

$$y+3=y+2\sqrt{y}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$y+3=y+2\sqrt{y}\sqrt{3}+3$$

Ikkala tarafdan y ni ayirish.

$$y+3-y=2\sqrt{y}\sqrt{3}+3$$

0 ni olish uchun y va -y ni birlashtirish.

$$3=2\sqrt{y}\sqrt{3}+3$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2\sqrt{y}\sqrt{3}+3=3$$

Ikkala tarafdan 3 ni ayirish.

$$2\sqrt{y}\sqrt{3}=3-3$$

0 olish uchun 3 dan 3 ni ayirish.

$$2\sqrt{y}\sqrt{3}=0$$

Ikki tarafini 2\sqrt{3} ga bo‘ling.

$$\frac{2\sqrt{3}\sqrt{y}}{2\sqrt{3}}=\frac{0}{2\sqrt{3}}$$

2\sqrt{3} ga bo'lish 2\sqrt{3} ga ko'paytirishni bekor qiladi.

$$\sqrt{y}=\frac{0}{2\sqrt{3}}$$

0 ni 2\sqrt{3} ga bo'lish.

$$\sqrt{y}=0$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$y=0$$

\sqrt{y+3}=\sqrt{y}+\sqrt{3} tenglamasida y uchun 0 ni almashtiring.

$$\sqrt{0+3}=\sqrt{0}+\sqrt{3}$$

Qisqartirish. y=0 tenglamani qoniqtiradi.

$$3^{\frac{1}{2}}=3^{\frac{1}{2}}$$

\sqrt{y+3}=\sqrt{y}+\sqrt{3} tenglamasi noyob yechimga ega.

$$y=0$$