a+bsqrt{2}=3(1-sqrt{2})+4sqrt{2} eching

$$a + b \sqrt { 2 } = 3 ( 1 - \sqrt { 2 } ) + 4 \sqrt { 2 }$$

b uchun yechish

$$b=-\frac{\sqrt{2}\left(a-\sqrt{2}-3\right)}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3 ga 1-\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a+b\sqrt{2}=3-3\sqrt{2}+4\sqrt{2}$$

\sqrt{2} ni olish uchun -3\sqrt{2} va 4\sqrt{2} ni birlashtirish.

$$a+b\sqrt{2}=3+\sqrt{2}$$

Ikkala tarafdan a ni ayirish.

$$b\sqrt{2}=3+\sqrt{2}-a$$

Tenglama standart shaklda.

$$\sqrt{2}b=-a+\sqrt{2}+3$$

Ikki tarafini \sqrt{2} ga bo‘ling.

$$\frac{\sqrt{2}b}{\sqrt{2}}=\frac{-a+\sqrt{2}+3}{\sqrt{2}}$$

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

$$b=\frac{-a+\sqrt{2}+3}{\sqrt{2}}$$

3+\sqrt{2}-a ni \sqrt{2} ga bo'lish.

$$b=\frac{\sqrt{2}\left(-a+\sqrt{2}+3\right)}{2}$$

a uchun yechish

$$a=-\sqrt{2}\left(b-1\right)+3$$