frac{{left(sqrt{3}+1+sqrt{3}-1right)}^2}{{left(sqrt{3}+1right)}^2-{left(sqrt{3}-1right)}^2} eching

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

Baholash

$$\sqrt{3}\approx 1,732050808$$

Yechim qadamlari

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

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

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

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

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\sqrt{3}+1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

4 olish uchun 3 va 1'ni qo'shing.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{3}-1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

\sqrt{3} kvadrati – 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

4 olish uchun 3 va 1'ni qo'shing.

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

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

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

0 olish uchun 4 dan 4 ni ayirish.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

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

$$\frac{12}{4\sqrt{3}}$$

\frac{12}{4\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Surat va maxrajdagi ikkala 3\times 4 ni qisqartiring.

$$\sqrt{3}$$

Kengaytirish

$$\sqrt{3} = 1,732050808$$

Yechim qadamlari

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

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

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

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

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\sqrt{3}+1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

4 olish uchun 3 va 1'ni qo'shing.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{3}-1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

\sqrt{3} kvadrati – 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

4 olish uchun 3 va 1'ni qo'shing.

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

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

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

0 olish uchun 4 dan 4 ni ayirish.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

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

$$\frac{12}{4\sqrt{3}}$$

\frac{12}{4\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Surat va maxrajdagi ikkala 3\times 4 ni qisqartiring.

$$\sqrt{3}$$