1/sqrt{5-2}-1/sqrt{5+2} eching

$$\frac { 1 } { \sqrt { 5 } - 2 } - \frac { 1 } { \sqrt { 5 } + 2 }$$

Baholash

$$4$$

Yechim qadamlari

\frac{1}{\sqrt{5}-2} maxrajini \sqrt{5}+2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{5}+2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}-\frac{1}{\sqrt{5}+2}$$

Hisoblang: \left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\sqrt{5}+2}{\left(\sqrt{5}\right)^{2}-2^{2}}-\frac{1}{\sqrt{5}+2}$$

\sqrt{5} kvadratini chiqarish. 2 kvadratini chiqarish.

$$\frac{\sqrt{5}+2}{5-4}-\frac{1}{\sqrt{5}+2}$$

1 olish uchun 5 dan 4 ni ayirish.

$$\frac{\sqrt{5}+2}{1}-\frac{1}{\sqrt{5}+2}$$

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

$$\sqrt{5}+2-\frac{1}{\sqrt{5}+2}$$

\frac{1}{\sqrt{5}+2} maxrajini \sqrt{5}-2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\sqrt{5}+2-\frac{\sqrt{5}-2}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}$$

Hisoblang: \left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\sqrt{5}+2-\frac{\sqrt{5}-2}{\left(\sqrt{5}\right)^{2}-2^{2}}$$

\sqrt{5} kvadratini chiqarish. 2 kvadratini chiqarish.

$$\sqrt{5}+2-\frac{\sqrt{5}-2}{5-4}$$

1 olish uchun 5 dan 4 ni ayirish.

$$\sqrt{5}+2-\frac{\sqrt{5}-2}{1}$$

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

$$\sqrt{5}+2-\left(\sqrt{5}-2\right)$$

\sqrt{5}-2 teskarisini topish uchun har birining teskarisini toping.

$$\sqrt{5}+2-\sqrt{5}-\left(-2\right)$$

-2 ning teskarisi 2 ga teng.

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

0 ni olish uchun \sqrt{5} va -\sqrt{5} ni birlashtirish.

$$2+2$$

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

$$4$$

Omil

$$2^{2}$$