(4sqrt{2}-3sqrt{6})(2sqrt{6}+3sqrt{2}) eching

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

Baholash

$$-2\sqrt{3}-12\approx -15,464101615$$

Yechim qadamlari

4\sqrt{2}-3\sqrt{6} ifodaning har bir elementini 2\sqrt{6}+3\sqrt{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$8\sqrt{2}\sqrt{6}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

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

$$8\sqrt{2}\sqrt{2}\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$8\times 2\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

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

$$16\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

\sqrt{2} kvadrati – 2.

$$16\sqrt{3}+12\times 2-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$16\sqrt{3}+24-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

\sqrt{6} kvadrati – 6.

$$16\sqrt{3}+24-6\times 6-9\sqrt{6}\sqrt{2}$$

-36 hosil qilish uchun -6 va 6 ni ko'paytirish.

$$16\sqrt{3}+24-36-9\sqrt{6}\sqrt{2}$$

-12 olish uchun 24 dan 36 ni ayirish.

$$16\sqrt{3}-12-9\sqrt{6}\sqrt{2}$$

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

$$16\sqrt{3}-12-9\sqrt{2}\sqrt{3}\sqrt{2}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$16\sqrt{3}-12-9\times 2\sqrt{3}$$

-18 hosil qilish uchun -9 va 2 ni ko'paytirish.

$$16\sqrt{3}-12-18\sqrt{3}$$

-2\sqrt{3} ni olish uchun 16\sqrt{3} va -18\sqrt{3} ni birlashtirish.

$$-2\sqrt{3}-12$$

Omil

$$2 {(-\sqrt{3} - 6)} = -15,464101615$$