12left(120-175right)/12+frac{2*10{sqrt{3}}} eching

$$\frac{ 12 \left( 120-175 \right) }{ 12+ \frac{ 2 \cdot 10 }{ \sqrt{ 3 } } }$$

Baholash

$$\frac{825\sqrt{3}-1485}{2}\approx -28,029041878$$

Qisqa yechim qadamlari

-55 olish uchun 120 dan 175 ni ayirish.

$$\frac{12\left(-55\right)}{12+\frac{2\times 10}{\sqrt{3}}}$$

-660 hosil qilish uchun 12 va -55 ni ko'paytirish.

$$\frac{-660}{12+\frac{2\times 10}{\sqrt{3}}}$$

20 hosil qilish uchun 2 va 10 ni ko'paytirish.

$$\frac{-660}{12+\frac{20}{\sqrt{3}}}$$

\frac{20}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{-660}{12+\frac{20\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

\sqrt{3} kvadrati – 3.

$$\frac{-660}{12+\frac{20\sqrt{3}}{3}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 12 ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{-660}{\frac{12\times 3}{3}+\frac{20\sqrt{3}}{3}}$$

\frac{12\times 3}{3} va \frac{20\sqrt{3}}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-660}{\frac{12\times 3+20\sqrt{3}}{3}}$$

12\times 3+20\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{-660}{\frac{36+20\sqrt{3}}{3}}$$

-660 ni \frac{36+20\sqrt{3}}{3} ga bo'lish -660 ga k'paytirish \frac{36+20\sqrt{3}}{3} ga qaytarish.

$$\frac{-660\times 3}{36+20\sqrt{3}}$$

\frac{-660\times 3}{36+20\sqrt{3}} maxrajini 36-20\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{-660\times 3\left(36-20\sqrt{3}\right)}{\left(36+20\sqrt{3}\right)\left(36-20\sqrt{3}\right)}$$

Hisoblang: \left(36+20\sqrt{3}\right)\left(36-20\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-660\times 3\left(36-20\sqrt{3}\right)}{36^{2}-\left(20\sqrt{3}\right)^{2}}$$

-1980 hosil qilish uchun -660 va 3 ni ko'paytirish.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{36^{2}-\left(20\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 36 ga hisoblang va 1296 ni qiymatni oling.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-\left(20\sqrt{3}\right)^{2}}$$

\left(20\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-20^{2}\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-400\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-400\times 3}$$

1200 hosil qilish uchun 400 va 3 ni ko'paytirish.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-1200}$$

96 olish uchun 1296 dan 1200 ni ayirish.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{96}$$

-\frac{165}{8}\left(36-20\sqrt{3}\right) ni olish uchun -1980\left(36-20\sqrt{3}\right) ni 96 ga bo‘ling.

$$-\frac{165}{8}\left(36-20\sqrt{3}\right)$$

-\frac{165}{8} ga 36-20\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{165}{8}\times 36-\frac{165}{8}\left(-20\right)\sqrt{3}$$

-\frac{165}{8}\times 36 ni yagona kasrga aylantiring.

$$\frac{-165\times 36}{8}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

-5940 hosil qilish uchun -165 va 36 ni ko'paytirish.

$$\frac{-5940}{8}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

\frac{-5940}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1485}{2}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

-\frac{165}{8}\left(-20\right) ni yagona kasrga aylantiring.

$$-\frac{1485}{2}+\frac{-165\left(-20\right)}{8}\sqrt{3}$$

3300 hosil qilish uchun -165 va -20 ni ko'paytirish.

$$-\frac{1485}{2}+\frac{3300}{8}\sqrt{3}$$

\frac{3300}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1485}{2}+\frac{825}{2}\sqrt{3}$$

Omil

$$\frac{165 {(5 \sqrt{3} - 9)}}{2} = -28,029041877838196$$