6sqrt{2}-6+12/10+6sqrt{2} eching

$$6 \sqrt { 2 } - 6 + \frac { 12 } { 10 + 6 \sqrt { 2 } }$$

Baholash

$$\frac{24\sqrt{2}-12}{7}\approx 3,1344465$$

Yechim qadamlari

\frac{12}{10+6\sqrt{2}} maxrajini 10-6\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{\left(10+6\sqrt{2}\right)\left(10-6\sqrt{2}\right)}$$

Hisoblang: \left(10+6\sqrt{2}\right)\left(10-6\sqrt{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{10^{2}-\left(6\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 10 ga hisoblang va 100 ni qiymatni oling.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-\left(6\sqrt{2}\right)^{2}}$$

\left(6\sqrt{2}\right)^{2} ni kengaytirish.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-6^{2}\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-36\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-36\times 2}$$

72 hosil qilish uchun 36 va 2 ni ko'paytirish.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-72}$$

28 olish uchun 100 dan 72 ni ayirish.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{28}$$

\frac{3}{7}\left(10-6\sqrt{2}\right) ni olish uchun 12\left(10-6\sqrt{2}\right) ni 28 ga bo‘ling.

$$6\sqrt{2}-6+\frac{3}{7}\left(10-6\sqrt{2}\right)$$

\frac{3}{7} ga 10-6\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6\sqrt{2}-6+\frac{3}{7}\times 10+\frac{3}{7}\left(-6\right)\sqrt{2}$$

\frac{3}{7}\times 10 ni yagona kasrga aylantiring.

$$6\sqrt{2}-6+\frac{3\times 10}{7}+\frac{3}{7}\left(-6\right)\sqrt{2}$$

30 hosil qilish uchun 3 va 10 ni ko'paytirish.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{3}{7}\left(-6\right)\sqrt{2}$$

\frac{3}{7}\left(-6\right) ni yagona kasrga aylantiring.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{3\left(-6\right)}{7}\sqrt{2}$$

-18 hosil qilish uchun 3 va -6 ni ko'paytirish.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{-18}{7}\sqrt{2}$$

\frac{-18}{7} kasri manfiy belgini olib tashlash bilan -\frac{18}{7} sifatida qayta yozilishi mumkin.

$$6\sqrt{2}-6+\frac{30}{7}-\frac{18}{7}\sqrt{2}$$

-6 ni -\frac{42}{7} kasrga o‘giring.

$$6\sqrt{2}-\frac{42}{7}+\frac{30}{7}-\frac{18}{7}\sqrt{2}$$

-\frac{42}{7} va \frac{30}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$6\sqrt{2}+\frac{-42+30}{7}-\frac{18}{7}\sqrt{2}$$

-12 olish uchun -42 va 30'ni qo'shing.

$$6\sqrt{2}-\frac{12}{7}-\frac{18}{7}\sqrt{2}$$

\frac{24}{7}\sqrt{2} ni olish uchun 6\sqrt{2} va -\frac{18}{7}\sqrt{2} ni birlashtirish.

$$\frac{24}{7}\sqrt{2}-\frac{12}{7}$$

Omil

$$\frac{12 {(2 \sqrt{2} - 1)}}{7} = 3,134446499564898$$