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

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

Baholash

$$6-8\sqrt{3}\approx -7,856406461$$

Yechim qadamlari

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

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

\sqrt{3} kvadrati – 3.

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

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

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

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

$$13-4\sqrt{3}-\left(\sqrt{3}+2\right)^{2}$$

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

$$13-4\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4\right)$$

\sqrt{3} kvadrati – 3.

$$13-4\sqrt{3}-\left(3+4\sqrt{3}+4\right)$$

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

$$13-4\sqrt{3}-\left(7+4\sqrt{3}\right)$$

7+4\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$13-4\sqrt{3}-7-4\sqrt{3}$$

6 olish uchun 13 dan 7 ni ayirish.

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

-8\sqrt{3} ni olish uchun -4\sqrt{3} va -4\sqrt{3} ni birlashtirish.

$$6-8\sqrt{3}$$

Kengaytirish

$$6-8\sqrt{3}$$

Yechim qadamlari

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

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

\sqrt{3} kvadrati – 3.

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

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

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

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

$$13-4\sqrt{3}-\left(\sqrt{3}+2\right)^{2}$$

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

$$13-4\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4\right)$$

\sqrt{3} kvadrati – 3.

$$13-4\sqrt{3}-\left(3+4\sqrt{3}+4\right)$$

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

$$13-4\sqrt{3}-\left(7+4\sqrt{3}\right)$$

7+4\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$13-4\sqrt{3}-7-4\sqrt{3}$$

6 olish uchun 13 dan 7 ni ayirish.

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

-8\sqrt{3} ni olish uchun -4\sqrt{3} va -4\sqrt{3} ni birlashtirish.

$$6-8\sqrt{3}$$