2/sqrt{2/2}=b/frac{sqrt{2+sqrt{6}}{4}} eching

$$\frac { 2 } { \frac { \sqrt { 2 } } { 2 } } = \frac { b } { \frac { \sqrt { 2 } + \sqrt { 6 } } { 4 } }$$

b uchun yechish

$$b=\sqrt{3}+1\approx 2,732050808$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 ni \frac{\sqrt{2}}{2} ga bo'lish 2 ga k'paytirish \frac{\sqrt{2}}{2} ga qaytarish.

$$\frac{2\times 2}{\sqrt{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{4}{\sqrt{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

\frac{4}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{4\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

\sqrt{2} kvadrati – 2.

$$\frac{4\sqrt{2}}{2}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

2\sqrt{2} ni olish uchun 4\sqrt{2} ni 2 ga bo‘ling.

$$2\sqrt{2}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

b ni \frac{\sqrt{2}+\sqrt{6}}{4} ga bo'lish b ga k'paytirish \frac{\sqrt{2}+\sqrt{6}}{4} ga qaytarish.

$$2\sqrt{2}=\frac{b\times 4}{\sqrt{2}+\sqrt{6}}$$

\frac{b\times 4}{\sqrt{2}+\sqrt{6}} maxrajini \sqrt{2}-\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right)}$$

Hisoblang: \left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{6}\right)^{2}}$$

\sqrt{2} kvadratini chiqarish. \sqrt{6} kvadratini chiqarish.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{2-6}$$

-4 olish uchun 2 dan 6 ni ayirish.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{-4}$$

-4 va -4 ni qisqartiring.

$$2\sqrt{2}=b\left(-1\right)\left(\sqrt{2}-\sqrt{6}\right)$$

b\left(-1\right) ga \sqrt{2}-\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2\sqrt{2}=-b\sqrt{2}+b\sqrt{6}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-b\sqrt{2}+b\sqrt{6}=2\sqrt{2}$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-\sqrt{2}+\sqrt{6}\right)b=2\sqrt{2}$$

Tenglama standart shaklda.

$$\left(\sqrt{6}-\sqrt{2}\right)b=2\sqrt{2}$$

Ikki tarafini -\sqrt{2}+\sqrt{6} ga bo‘ling.

$$\frac{\left(\sqrt{6}-\sqrt{2}\right)b}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{2}}{\sqrt{6}-\sqrt{2}}$$

-\sqrt{2}+\sqrt{6} ga bo'lish -\sqrt{2}+\sqrt{6} ga ko'paytirishni bekor qiladi.

$$b=\frac{2\sqrt{2}}{\sqrt{6}-\sqrt{2}}$$

2\sqrt{2} ni -\sqrt{2}+\sqrt{6} ga bo'lish.

$$b=\sqrt{3}+1$$