frac{3/2+sqrt{3}-2/2-sqrt{3}}{2-5sqrt{3}} eching

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

Baholash

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Yechim qadamlari

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

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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}.

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{4-3}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{\frac{3\left(2-\sqrt{3}\right)}{1}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}}{2-5\sqrt{3}}$$

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}.

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{4-3}}{2-5\sqrt{3}}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{3\left(2-\sqrt{3}\right)-\frac{2\left(2+\sqrt{3}\right)}{1}}{2-5\sqrt{3}}$$

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

$$\frac{3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)}{2-5\sqrt{3}}$$

\frac{3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)}{2-5\sqrt{3}} maxrajini 2+5\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{\left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right)}$$

Hisoblang: \left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{2^{2}-\left(-5\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-\left(-5\sqrt{3}\right)^{2}}$$

\left(-5\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-\left(-5\right)^{2}\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini -5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-25\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-25\times 3}$$

75 hosil qilish uchun 25 va 3 ni ko'paytirish.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{4-75}$$

-71 olish uchun 4 dan 75 ni ayirish.

$$\frac{\left(3\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

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

$$\frac{\left(6-3\sqrt{3}-2\left(2+\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

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

$$\frac{\left(6-3\sqrt{3}-\left(4+2\sqrt{3}\right)\right)\left(2+5\sqrt{3}\right)}{-71}$$

4+2\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$\frac{\left(6-3\sqrt{3}-4-2\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

2 olish uchun 6 dan 4 ni ayirish.

$$\frac{\left(2-3\sqrt{3}-2\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

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

$$\frac{\left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right)}{-71}$$

Hisoblang: \left(2-5\sqrt{3}\right)\left(2+5\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2^{2}-\left(5\sqrt{3}\right)^{2}}{-71}$$

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

$$\frac{4-\left(5\sqrt{3}\right)^{2}}{-71}$$

\left(5\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{4-5^{2}\left(\sqrt{3}\right)^{2}}{-71}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{4-25\left(\sqrt{3}\right)^{2}}{-71}$$

\sqrt{3} kvadrati – 3.

$$\frac{4-25\times 3}{-71}$$

75 hosil qilish uchun 25 va 3 ni ko'paytirish.

$$\frac{4-75}{-71}$$

-71 olish uchun 4 dan 75 ni ayirish.

$$\frac{-71}{-71}$$

1 ni olish uchun -71 ni -71 ga bo‘ling.

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Omil

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