frac{3sqrt{3}-2}{2sqrt{7}+1} eching

$$\frac { 3 \sqrt { 3 } - 2 } { 2 \sqrt { 7 } + 1 }$$

Baholash

$$\frac{2\sqrt{21}}{9}-\frac{\sqrt{3}}{9}-\frac{4\sqrt{7}}{27}+\frac{2}{27}\approx 0,508010982$$

Yechim qadamlari

\frac{3\sqrt{3}-2}{2\sqrt{7}+1} maxrajini 2\sqrt{7}-1 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{\left(2\sqrt{7}+1\right)\left(2\sqrt{7}-1\right)}$$

Hisoblang: \left(2\sqrt{7}+1\right)\left(2\sqrt{7}-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{\left(2\sqrt{7}\right)^{2}-1^{2}}$$

\left(2\sqrt{7}\right)^{2} ni kengaytirish.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{2^{2}\left(\sqrt{7}\right)^{2}-1^{2}}$$

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

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{4\left(\sqrt{7}\right)^{2}-1^{2}}$$

\sqrt{7} kvadrati – 7.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{4\times 7-1^{2}}$$

28 hosil qilish uchun 4 va 7 ni ko'paytirish.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{28-1^{2}}$$

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{28-1}$$

27 olish uchun 28 dan 1 ni ayirish.

$$\frac{\left(3\sqrt{3}-2\right)\left(2\sqrt{7}-1\right)}{27}$$

3\sqrt{3}-2 ifodaning har bir elementini 2\sqrt{7}-1 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{6\sqrt{3}\sqrt{7}-3\sqrt{3}-4\sqrt{7}+2}{27}$$

\sqrt{3} va \sqrt{7} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{6\sqrt{21}-3\sqrt{3}-4\sqrt{7}+2}{27}$$