12/3+sqrt{3}-8+2sqrt{3} eching

$$\frac { 12 } { 3 + \sqrt { 3 } } - 8 + 2 \sqrt { 3 }$$

Baholash

$$-2$$

Yechim qadamlari

\frac{12}{3+\sqrt{3}} maxrajini 3-\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{12\left(3-\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}-8+2\sqrt{3}$$

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

$$\frac{12\left(3-\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}-8+2\sqrt{3}$$

3 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{12\left(3-\sqrt{3}\right)}{9-3}-8+2\sqrt{3}$$

6 olish uchun 9 dan 3 ni ayirish.

$$\frac{12\left(3-\sqrt{3}\right)}{6}-8+2\sqrt{3}$$

2\left(3-\sqrt{3}\right) ni olish uchun 12\left(3-\sqrt{3}\right) ni 6 ga bo‘ling.

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

2 ga 3-\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6-2\sqrt{3}-8+2\sqrt{3}$$

-2 olish uchun 6 dan 8 ni ayirish.

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

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

$$-2$$

Omil

$$-2$$