5/4-sqrt{11}-4/sqrt{11-sqrt{7}}-2/3+sqrt{7} eching

$$\frac { 5 } { 4 - \sqrt { 11 } } - \frac { 4 } { \sqrt { 11 } - \sqrt { 7 } } - \frac { 2 } { 3 + \sqrt { 7 } }$$

Baholash

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Yechim qadamlari

\frac{5}{4-\sqrt{11}} maxrajini 4+\sqrt{11} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{5\left(4+\sqrt{11}\right)}{\left(4-\sqrt{11}\right)\left(4+\sqrt{11}\right)}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Hisoblang: \left(4-\sqrt{11}\right)\left(4+\sqrt{11}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{5\left(4+\sqrt{11}\right)}{4^{2}-\left(\sqrt{11}\right)^{2}}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

4 kvadratini chiqarish. \sqrt{11} kvadratini chiqarish.

$$\frac{5\left(4+\sqrt{11}\right)}{16-11}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

5 olish uchun 16 dan 11 ni ayirish.

$$\frac{5\left(4+\sqrt{11}\right)}{5}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

5 va 5 ni qisqartiring.

$$4+\sqrt{11}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

\frac{4}{\sqrt{11}-\sqrt{7}} maxrajini \sqrt{11}+\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)}-\frac{2}{3+\sqrt{7}}$$

Hisoblang: \left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{\left(\sqrt{11}\right)^{2}-\left(\sqrt{7}\right)^{2}}-\frac{2}{3+\sqrt{7}}$$

\sqrt{11} kvadratini chiqarish. \sqrt{7} kvadratini chiqarish.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{11-7}-\frac{2}{3+\sqrt{7}}$$

4 olish uchun 11 dan 7 ni ayirish.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{4}-\frac{2}{3+\sqrt{7}}$$

4 va 4 ni qisqartiring.

$$4+\sqrt{11}-\left(\sqrt{11}+\sqrt{7}\right)-\frac{2}{3+\sqrt{7}}$$

\sqrt{11}+\sqrt{7} teskarisini topish uchun har birining teskarisini toping.

$$4+\sqrt{11}-\sqrt{11}-\sqrt{7}-\frac{2}{3+\sqrt{7}}$$

0 ni olish uchun \sqrt{11} va -\sqrt{11} ni birlashtirish.

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

\frac{2}{3+\sqrt{7}} maxrajini 3-\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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}.

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

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

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

2 olish uchun 9 dan 7 ni ayirish.

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

2 va 2 ni qisqartiring.

$$4-\sqrt{7}-\left(3-\sqrt{7}\right)$$

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

$$4-\sqrt{7}-3-\left(-\sqrt{7}\right)$$

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

$$4-\sqrt{7}-3+\sqrt{7}$$

1 olish uchun 4 dan 3 ni ayirish.

$$1-\sqrt{7}+\sqrt{7}$$

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

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Omil

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