5/-5-3sqrt{3} eching

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

Baholash

$$\frac{25-15\sqrt{3}}{2}\approx -0,490381057$$

Yechim qadamlari

\frac{5}{-5-3\sqrt{3}} maxrajini -5+3\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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

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

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

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

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

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

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

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-9\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-9\times 3}$$

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

$$\frac{5\left(-5+3\sqrt{3}\right)}{25-27}$$

-2 olish uchun 25 dan 27 ni ayirish.

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

5 ga -5+3\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{-25+15\sqrt{3}}{-2}$$