3/2-sqrt{3}+4/sqrt{3+1} eching

$$\frac { 3 } { 2 - \sqrt { 3 } } + \frac { 4 } { \sqrt { 3 } + 1 }$$

Baholash

$$5\sqrt{3}+4\approx 12,660254038$$

Yechim qadamlari

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

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

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

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

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

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

1 olish uchun 4 dan 3 ni ayirish.

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

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

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

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

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

Hisoblang: \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\sqrt{3} kvadratini chiqarish. 1 kvadratini chiqarish.

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

2 olish uchun 3 dan 1 ni ayirish.

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

2\left(\sqrt{3}-1\right) ni olish uchun 4\left(\sqrt{3}-1\right) ni 2 ga bo‘ling.

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

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

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

2 ga \sqrt{3}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

$$6+5\sqrt{3}-2$$

4 olish uchun 6 dan 2 ni ayirish.

$$4+5\sqrt{3}$$