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

$$( 7 + \sqrt { 3 } ) ( 2 - \sqrt { 3 } ) ^ { 2 } + ( 2 ^ { 2 } - 3 ) + \sqrt { 3 }$$

Baholash

$$38-20\sqrt{3}\approx 3,358983849$$

Yechim qadamlari

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

$$\left(7+\sqrt{3}\right)\left(4-4\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)+2^{2}-3+\sqrt{3}$$

\sqrt{3} kvadrati – 3.

$$\left(7+\sqrt{3}\right)\left(4-4\sqrt{3}+3\right)+2^{2}-3+\sqrt{3}$$

7 olish uchun 4 va 3'ni qo'shing.

$$\left(7+\sqrt{3}\right)\left(7-4\sqrt{3}\right)+2^{2}-3+\sqrt{3}$$

7+\sqrt{3} ga 7-4\sqrt{3} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$49-21\sqrt{3}-4\left(\sqrt{3}\right)^{2}+2^{2}-3+\sqrt{3}$$

\sqrt{3} kvadrati – 3.

$$49-21\sqrt{3}-4\times 3+2^{2}-3+\sqrt{3}$$

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

$$49-21\sqrt{3}-12+2^{2}-3+\sqrt{3}$$

37 olish uchun 49 dan 12 ni ayirish.

$$37-21\sqrt{3}+2^{2}-3+\sqrt{3}$$

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

$$37-21\sqrt{3}+4-3+\sqrt{3}$$

41 olish uchun 37 va 4'ni qo'shing.

$$41-21\sqrt{3}-3+\sqrt{3}$$

38 olish uchun 41 dan 3 ni ayirish.

$$38-21\sqrt{3}+\sqrt{3}$$

-20\sqrt{3} ni olish uchun -21\sqrt{3} va \sqrt{3} ni birlashtirish.

$$38-20\sqrt{3}$$