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

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

Baholash

$$10$$

Yechim qadamlari

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

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

\sqrt{3} kvadrati – 3.

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

4 olish uchun 1 va 3'ni qo'shing.

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

2 ga 3+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4-2\sqrt{3}+6+2\sqrt{3}$$

10 olish uchun 4 va 6'ni qo'shing.

$$10-2\sqrt{3}+2\sqrt{3}$$

0 ni olish uchun -2\sqrt{3} va 2\sqrt{3} ni birlashtirish.

$$10$$

Omil

$$2\times 5$$