frac{3-2sqrt{12}}{1-3sqrt{3}} eching

$$\frac { 3 - 2 \sqrt { 12 } } { 1 - 3 \sqrt { 3 } }$$

Baholash

$$\frac{33-5\sqrt{3}}{26}\approx 0,936144075$$

Yechim qadamlari

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{3-2\times 2\sqrt{3}}{1-3\sqrt{3}}$$

-4 hosil qilish uchun -2 va 2 ni ko'paytirish.

$$\frac{3-4\sqrt{3}}{1-3\sqrt{3}}$$

\frac{3-4\sqrt{3}}{1-3\sqrt{3}} maxrajini 1+3\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(1-3\sqrt{3}\right)\left(1+3\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

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

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

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

2 daraja ko‘rsatkichini -3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{\left(3-4\sqrt{3}\right)\left(1+3\sqrt{3}\right)}{1-9\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\left(3-4\sqrt{3}\right)\left(1+3\sqrt{3}\right)}{1-9\times 3}$$

27 hosil qilish uchun 9 va 3 ni ko'paytirish.

$$\frac{\left(3-4\sqrt{3}\right)\left(1+3\sqrt{3}\right)}{1-27}$$

-26 olish uchun 1 dan 27 ni ayirish.

$$\frac{\left(3-4\sqrt{3}\right)\left(1+3\sqrt{3}\right)}{-26}$$

3-4\sqrt{3} ifodaning har bir elementini 1+3\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{3+9\sqrt{3}-4\sqrt{3}-12\left(\sqrt{3}\right)^{2}}{-26}$$

5\sqrt{3} ni olish uchun 9\sqrt{3} va -4\sqrt{3} ni birlashtirish.

$$\frac{3+5\sqrt{3}-12\left(\sqrt{3}\right)^{2}}{-26}$$

\sqrt{3} kvadrati – 3.

$$\frac{3+5\sqrt{3}-12\times 3}{-26}$$

-36 hosil qilish uchun -12 va 3 ni ko'paytirish.

$$\frac{3+5\sqrt{3}-36}{-26}$$

-33 olish uchun 3 dan 36 ni ayirish.

$$\frac{-33+5\sqrt{3}}{-26}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{33-5\sqrt{3}}{26}$$