frac{2sqrt{3}-sqrt{2}}{2sqrt{3}+sqrt{2}} eching

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

Baholash

$$\frac{7-2\sqrt{6}}{5}\approx 0,420204103$$

Yechim qadamlari

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

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

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

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

\left(2\sqrt{3}-\sqrt{2}\right)^{2} hosil qilish uchun 2\sqrt{3}-\sqrt{2} va 2\sqrt{3}-\sqrt{2} ni ko'paytirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2\sqrt{3}-\sqrt{2}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{3} kvadrati – 3.

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

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{12-4\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{12-4\sqrt{6}+\left(\sqrt{2}\right)^{2}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{12-4\sqrt{6}+2}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

14 olish uchun 12 va 2'ni qo'shing.

$$\frac{14-4\sqrt{6}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\left(2\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{14-4\sqrt{6}}{2^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{14-4\sqrt{6}}{4\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{14-4\sqrt{6}}{4\times 3-\left(\sqrt{2}\right)^{2}}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{14-4\sqrt{6}}{12-\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{14-4\sqrt{6}}{12-2}$$

10 olish uchun 12 dan 2 ni ayirish.

$$\frac{14-4\sqrt{6}}{10}$$

Omil

$$\frac{7 - 2 \sqrt{6}}{5} = 0,4202041028867288$$