frac{sqrt{2}left(4-sqrt{2}right)}{2left(sqrt{2}+1right)} eching

$$\frac{ \sqrt{ 2 } \left( 4- \sqrt{ 2 } \right) }{ 2 \left( \sqrt{ 2 } +1 \right) }$$

Baholash

$$5-3\sqrt{2}\approx 0,757359313$$

Yechim qadamlari

\sqrt{2} ga 4-\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{4\sqrt{2}-\left(\sqrt{2}\right)^{2}}{2\left(\sqrt{2}+1\right)}$$

\sqrt{2} kvadrati – 2.

$$\frac{4\sqrt{2}-2}{2\left(\sqrt{2}+1\right)}$$

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

$$\frac{4\sqrt{2}-2}{2\sqrt{2}+2}$$

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{\left(2\sqrt{2}+2\right)\left(2\sqrt{2}-2\right)}$$

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{\left(2\sqrt{2}\right)^{2}-2^{2}}$$

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{2^{2}\left(\sqrt{2}\right)^{2}-2^{2}}$$

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{4\left(\sqrt{2}\right)^{2}-2^{2}}$$

\sqrt{2} kvadrati – 2.

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

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{8-2^{2}}$$

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

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{8-4}$$

4 olish uchun 8 dan 4 ni ayirish.

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{4}$$

4\sqrt{2}-2 ifodaning har bir elementini 2\sqrt{2}-2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{8\left(\sqrt{2}\right)^{2}-8\sqrt{2}-4\sqrt{2}+4}{4}$$

\sqrt{2} kvadrati – 2.

$$\frac{8\times 2-8\sqrt{2}-4\sqrt{2}+4}{4}$$

16 hosil qilish uchun 8 va 2 ni ko'paytirish.

$$\frac{16-8\sqrt{2}-4\sqrt{2}+4}{4}$$

-12\sqrt{2} ni olish uchun -8\sqrt{2} va -4\sqrt{2} ni birlashtirish.

$$\frac{16-12\sqrt{2}+4}{4}$$

20 olish uchun 16 va 4'ni qo'shing.

$$\frac{20-12\sqrt{2}}{4}$$

5-3\sqrt{2} natijani olish uchun 20-12\sqrt{2} ning har bir ifodasini 4 ga bo‘ling.

$$5-3\sqrt{2}$$