(2+sqrt{3})^2+(2-sqrt{3})^2+16 eching

$$( 2 + \sqrt { 3 } ) ^ { 2 } + ( 2 - \sqrt { 3 } ) ^ { 2 } + 16$$

Baholash

$$30$$

Yechim qadamlari

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

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

\sqrt{3} kvadrati – 3.

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

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

$$7+4\sqrt{3}+\left(2-\sqrt{3}\right)^{2}+16$$

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

$$7+4\sqrt{3}+4-4\sqrt{3}+\left(\sqrt{3}\right)^{2}+16$$

\sqrt{3} kvadrati – 3.

$$7+4\sqrt{3}+4-4\sqrt{3}+3+16$$

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

$$7+4\sqrt{3}+7-4\sqrt{3}+16$$

14 olish uchun 7 va 7'ni qo'shing.

$$14+4\sqrt{3}-4\sqrt{3}+16$$

0 ni olish uchun 4\sqrt{3} va -4\sqrt{3} ni birlashtirish.

$$14+16$$

30 olish uchun 14 va 16'ni qo'shing.

$$30$$

Omil

$$2\times 3\times 5$$