7-4sqrt{3}+1/7-4sqrt{3} eching

$$7-4 \sqrt{ 3 } + \frac{ 1 }{ 7-4 \sqrt{ 3 } }$$

Baholash

$$14$$

Yechim qadamlari

\frac{1}{7-4\sqrt{3}} maxrajini 7+4\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{\left(7-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)}$$

Hisoblang: \left(7-4\sqrt{3}\right)\left(7+4\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{49-\left(-4\sqrt{3}\right)^{2}}$$

\left(-4\sqrt{3}\right)^{2} ni kengaytirish.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{49-\left(-4\right)^{2}\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini -4 ga hisoblang va 16 ni qiymatni oling.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{49-16\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{49-16\times 3}$$

48 hosil qilish uchun 16 va 3 ni ko'paytirish.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{49-48}$$

1 olish uchun 49 dan 48 ni ayirish.

$$7-4\sqrt{3}+\frac{7+4\sqrt{3}}{1}$$

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

$$7-4\sqrt{3}+7+4\sqrt{3}$$

14 olish uchun 7 va 7'ni qo'shing.

$$14-4\sqrt{3}+4\sqrt{3}$$

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

$$14$$

Omil

$$2\times 7$$