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

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

Baholash

$$2\sqrt{3}\approx 3,464101615$$

Yechim qadamlari

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

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

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

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

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

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

-1 olish uchun 3 dan 4 ni ayirish.

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

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi. \sqrt{3}-2 teskarisini topish uchun har birining teskarisini toping.

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

-\sqrt{3}-\left(-2\right) teskarisini topish uchun har birining teskarisini toping.

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

-\sqrt{3} ning teskarisi \sqrt{3} ga teng.

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

-2 ning teskarisi 2 ga teng.

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

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

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

0 olish uchun 2 dan 2 ni ayirish.

$$2\sqrt{3}$$