(2sqrt{2}-1)^2-(1+sqrt{3})*(sqrt{2}-sqrt{6}) eching

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } - ( 1 + \sqrt { 3 } ) \times ( \sqrt { 2 } - \sqrt { 6 } )$$

Baholash

$$9-2\sqrt{2}\approx 6,171572875$$

Yechim qadamlari

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

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

\sqrt{2} kvadrati – 2.

$$4\times 2-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$8-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

9 olish uchun 8 va 1'ni qo'shing.

$$9-4\sqrt{2}-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

1+\sqrt{3} ga \sqrt{2}-\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{3}\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{6}-\sqrt{3}\sqrt{6}\right)$$

0 ni olish uchun -\sqrt{6} va \sqrt{6} ni birlashtirish.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{3}\sqrt{2}\right)$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$9-4\sqrt{2}-\left(\sqrt{2}-3\sqrt{2}\right)$$

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

$$9-4\sqrt{2}-\left(-2\sqrt{2}\right)$$

-2\sqrt{2} ning teskarisi 2\sqrt{2} ga teng.

$$9-4\sqrt{2}+2\sqrt{2}$$

-2\sqrt{2} ni olish uchun -4\sqrt{2} va 2\sqrt{2} ni birlashtirish.

$$9-2\sqrt{2}$$