frac{3+2sqrt{2}}{2+sqrt{2}}*frac{sqrt{2}-1}{sqrt{2}} eching

$$\frac { 3 + 2 \sqrt { 2 } } { 2 + \sqrt { 2 } } \cdot \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } }$$

Baholash

$$\frac{1}{2}=0,5$$

Yechim qadamlari

\frac{3+2\sqrt{2}}{2+\sqrt{2}} maxrajini 2-\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

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

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2^{2}-\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

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

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{4-2}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

2 olish uchun 4 dan 2 ni ayirish.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

\frac{\sqrt{2}-1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2} ni \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{2} ga ko‘paytiring.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{2\times 2}$$

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

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

3+2\sqrt{2} ifodaning har bir elementini 2-\sqrt{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\left(6-3\sqrt{2}+4\sqrt{2}-2\left(\sqrt{2}\right)^{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

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

$$\frac{\left(6+\sqrt{2}-2\left(\sqrt{2}\right)^{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

\sqrt{2} kvadrati – 2.

$$\frac{\left(6+\sqrt{2}-2\times 2\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

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

$$\frac{\left(6+\sqrt{2}-4\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

2 olish uchun 6 dan 4 ni ayirish.

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

2+\sqrt{2} ifodaning har bir elementini \sqrt{2}-1 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

\sqrt{2} kvadrati – 2.

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

0 olish uchun -2 va 2'ni qo'shing.

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

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

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

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$\frac{2}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}$$

Omil

$$\frac{1}{2} = 0,5$$