1/2-sqrt{3}+1/2+sqrt{3}+frac{sqrt{8}}{sqrt{2}} eching

$$\frac { 1 } { 2 - \sqrt { 3 } } + \frac { 1 } { 2 + \sqrt { 3 } } + \frac { \sqrt { 8 } } { \sqrt { 2 } }$$

Baholash

$$6$$

Yechim qadamlari

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

$$\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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}.

$$\frac{2+\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

$$\frac{2+\sqrt{3}}{4-3}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{2+\sqrt{3}}{1}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

$$2+\sqrt{3}+\frac{1}{2+\sqrt{3}}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

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

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}.

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

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

$$2+\sqrt{3}+\frac{2-\sqrt{3}}{4-3}+\frac{\sqrt{8}}{\sqrt{2}}$$

1 olish uchun 4 dan 3 ni ayirish.

$$2+\sqrt{3}+\frac{2-\sqrt{3}}{1}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

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

4 olish uchun 2 va 2'ni qo'shing.

$$4+\sqrt{3}-\sqrt{3}+\frac{\sqrt{8}}{\sqrt{2}}$$

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

$$4+\frac{\sqrt{8}}{\sqrt{2}}$$

\frac{\sqrt{8}}{\sqrt{2}} kvadrat ildizlar boʻlinmasini \sqrt{\frac{8}{2}} boʻlinmasining kvadrat ildizi sifatida qayta yozing va boʻlishni amalga oshiring.

$$4+\sqrt{4}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$4+2$$

6 olish uchun 4 va 2'ni qo'shing.

$$6$$

Omil

$$2\times 3$$