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

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

Baholash

$$2-4\sqrt{3}\approx -4,92820323$$

Yechim qadamlari

Hisoblang: \left(1-2\sqrt{3}\right)\left(2\sqrt{3}+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

-11 olish uchun 1 dan 12 ni ayirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2\sqrt{3}-1\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{3} kvadrati – 3.

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

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

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

13 olish uchun 12 va 1'ni qo'shing.

$$-11+13-4\sqrt{3}$$

2 olish uchun -11 va 13'ni qo'shing.

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