9/sqrt{7-2}-4/3+sqrt{7}+5/sqrt{6-sqrt{7}} eching

$$\frac { 9 } { \sqrt { 7 } - 2 } - \frac { 4 } { 3 + \sqrt { 7 } } + \frac { 5 } { \sqrt { 6 } - \sqrt { 7 } }$$

Baholash

$$-5\sqrt{6}\approx -12,247448714$$

Yechim qadamlari

\frac{9}{\sqrt{7}-2} maxrajini \sqrt{7}+2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Hisoblang: \left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

\sqrt{7} kvadratini chiqarish. 2 kvadratini chiqarish.

$$\frac{9\left(\sqrt{7}+2\right)}{7-4}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

3 olish uchun 7 dan 4 ni ayirish.

$$\frac{9\left(\sqrt{7}+2\right)}{3}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

3\left(\sqrt{7}+2\right) ni olish uchun 9\left(\sqrt{7}+2\right) ni 3 ga bo‘ling.

$$3\left(\sqrt{7}+2\right)-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

\frac{4}{3+\sqrt{7}} maxrajini 3-\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Hisoblang: \left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

3 kvadratini chiqarish. \sqrt{7} kvadratini chiqarish.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{9-7}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

2 olish uchun 9 dan 7 ni ayirish.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{2}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

2\left(3-\sqrt{7}\right) ni olish uchun 4\left(3-\sqrt{7}\right) ni 2 ga bo‘ling.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5}{\sqrt{6}-\sqrt{7}}$$

\frac{5}{\sqrt{6}-\sqrt{7}} maxrajini \sqrt{6}+\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{\left(\sqrt{6}-\sqrt{7}\right)\left(\sqrt{6}+\sqrt{7}\right)}$$

Hisoblang: \left(\sqrt{6}-\sqrt{7}\right)\left(\sqrt{6}+\sqrt{7}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$

\sqrt{6} kvadratini chiqarish. \sqrt{7} kvadratini chiqarish.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{6-7}$$

-1 olish uchun 6 dan 7 ni ayirish.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{-1}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

3 ga \sqrt{7}+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3\sqrt{7}+6-2\left(3-\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

2 ga 3-\sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3\sqrt{7}+6-\left(6-2\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

6-2\sqrt{7} teskarisini topish uchun har birining teskarisini toping.

$$3\sqrt{7}+6-6-\left(-2\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

-2\sqrt{7} ning teskarisi 2\sqrt{7} ga teng.

$$3\sqrt{7}+6-6+2\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

0 olish uchun 6 dan 6 ni ayirish.

$$3\sqrt{7}+2\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

5\sqrt{7} ni olish uchun 3\sqrt{7} va 2\sqrt{7} ni birlashtirish.

$$5\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

-5 ga \sqrt{6}+\sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5\sqrt{7}-5\sqrt{6}-5\sqrt{7}$$

0 ni olish uchun 5\sqrt{7} va -5\sqrt{7} ni birlashtirish.

$$-5\sqrt{6}$$