(2sqrt{2}-1)^2+(2sqrt{3}-1)(-2sqrt{3}-1)+frac{sqrt{12}-3}{sqrt{3}} eching

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } + ( 2 \sqrt { 3 } - 1 ) ( - 2 \sqrt { 3 } - 1 ) + \frac { \sqrt { 12 } - 3 } { \sqrt { 3 } }$$

Baholash

$$-\sqrt{3}-4\sqrt{2}\approx -7,388905057$$

Qisqa yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2\sqrt{2}-1\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

\sqrt{2} kvadrati – 2.

$$4\times 2-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

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

$$8-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

9 olish uchun 8 va 1'ni qo'shing.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

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.

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

\frac{2\sqrt{3}-3}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9-4\sqrt{2} ni \frac{3}{3} marotabaga ko'paytirish.

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

\frac{3\left(9-4\sqrt{2}\right)}{3} va \frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

3\left(9-4\sqrt{2}\right)+\left(2\sqrt{3}-3\right)\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{27-12\sqrt{2}+6-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

27-12\sqrt{2}+6-3\sqrt{3} hisob-kitobini qiling.

$$\frac{33-12\sqrt{2}-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

11-4\sqrt{2}-\sqrt{3} natijani olish uchun 33-12\sqrt{2}-3\sqrt{3} ning har bir ifodasini 3 ga bo‘ling.

$$11-4\sqrt{2}-\sqrt{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

2\sqrt{3}-1 ga -2\sqrt{3}-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11-4\sqrt{2}-\sqrt{3}-4\left(\sqrt{3}\right)^{2}+1$$

\sqrt{3} kvadrati – 3.

$$11-4\sqrt{2}-\sqrt{3}-4\times 3+1$$

-12 hosil qilish uchun -4 va 3 ni ko'paytirish.

$$11-4\sqrt{2}-\sqrt{3}-12+1$$

-11 olish uchun -12 va 1'ni qo'shing.

$$11-4\sqrt{2}-\sqrt{3}-11$$

0 olish uchun 11 dan 11 ni ayirish.

$$-4\sqrt{2}-\sqrt{3}$$