frac{8+3sqrt{7}}{8-3sqrt{7}} eching

$$\frac { 8 + 3 \sqrt { 7 } } { 8 - 3 \sqrt { 7 } }$$

Baholash

$$48\sqrt{7}+127\approx 253,996062931$$

Yechim qadamlari

\frac{8+3\sqrt{7}}{8-3\sqrt{7}} maxrajini 8+3\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(8+3\sqrt{7}\right)\left(8+3\sqrt{7}\right)}{\left(8-3\sqrt{7}\right)\left(8+3\sqrt{7}\right)}$$

Hisoblang: \left(8-3\sqrt{7}\right)\left(8+3\sqrt{7}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(8+3\sqrt{7}\right)\left(8+3\sqrt{7}\right)}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

\left(8+3\sqrt{7}\right)^{2} hosil qilish uchun 8+3\sqrt{7} va 8+3\sqrt{7} ni ko'paytirish.

$$\frac{\left(8+3\sqrt{7}\right)^{2}}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(8+3\sqrt{7}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{64+48\sqrt{7}+9\left(\sqrt{7}\right)^{2}}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

\sqrt{7} kvadrati – 7.

$$\frac{64+48\sqrt{7}+9\times 7}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

63 hosil qilish uchun 9 va 7 ni ko'paytirish.

$$\frac{64+48\sqrt{7}+63}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

127 olish uchun 64 va 63'ni qo'shing.

$$\frac{127+48\sqrt{7}}{8^{2}-\left(-3\sqrt{7}\right)^{2}}$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$\frac{127+48\sqrt{7}}{64-\left(-3\sqrt{7}\right)^{2}}$$

\left(-3\sqrt{7}\right)^{2} ni kengaytirish.

$$\frac{127+48\sqrt{7}}{64-\left(-3\right)^{2}\left(\sqrt{7}\right)^{2}}$$

2 daraja ko‘rsatkichini -3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{127+48\sqrt{7}}{64-9\left(\sqrt{7}\right)^{2}}$$

\sqrt{7} kvadrati – 7.

$$\frac{127+48\sqrt{7}}{64-9\times 7}$$

63 hosil qilish uchun 9 va 7 ni ko'paytirish.

$$\frac{127+48\sqrt{7}}{64-63}$$

1 olish uchun 64 dan 63 ni ayirish.

$$\frac{127+48\sqrt{7}}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$127+48\sqrt{7}$$