4sqrt{3}-6-1/4sqrt{3-6}-1 eching

$$4 \sqrt { 3 } - 6 - \frac { 1 } { 4 \sqrt { 3 } - 6 } - 1$$

Baholash

$$\frac{11\sqrt{3}}{3}-\frac{15}{2}\approx -1,149147039$$

Qisqa yechim qadamlari

\frac{1}{4\sqrt{3}-6} maxrajini 4\sqrt{3}+6 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{\left(4\sqrt{3}-6\right)\left(4\sqrt{3}+6\right)}-1$$

Hisoblang: \left(4\sqrt{3}-6\right)\left(4\sqrt{3}+6\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{\left(4\sqrt{3}\right)^{2}-6^{2}}-1$$

\left(4\sqrt{3}\right)^{2} ni kengaytirish.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{4^{2}\left(\sqrt{3}\right)^{2}-6^{2}}-1$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{16\left(\sqrt{3}\right)^{2}-6^{2}}-1$$

\sqrt{3} kvadrati – 3.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{16\times 3-6^{2}}-1$$

48 hosil qilish uchun 16 va 3 ni ko'paytirish.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{48-6^{2}}-1$$

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

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{48-36}-1$$

12 olish uchun 48 dan 36 ni ayirish.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{12}-1$$

-7 olish uchun -6 dan 1 ni ayirish.

$$4\sqrt{3}-7-\frac{4\sqrt{3}+6}{12}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4\sqrt{3}-7 ni \frac{12}{12} marotabaga ko'paytirish.

$$\frac{12\left(4\sqrt{3}-7\right)}{12}-\frac{4\sqrt{3}+6}{12}$$

\frac{12\left(4\sqrt{3}-7\right)}{12} va \frac{4\sqrt{3}+6}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{12\left(4\sqrt{3}-7\right)-\left(4\sqrt{3}+6\right)}{12}$$

12\left(4\sqrt{3}-7\right)-\left(4\sqrt{3}+6\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{48\sqrt{3}-84-4\sqrt{3}-6}{12}$$

48\sqrt{3}-84-4\sqrt{3}-6 hisob-kitobini qiling.

$$\frac{44\sqrt{3}-90}{12}$$

Omil

$$\frac{22 \sqrt{3} - 45}{6} = -1,1491470389141167$$