19*(sqrt{5}-sqrt{3}+sqrt{2})(sqrt{5}-sqrt{3}-sqrt{2}) eching

$$19 \cdot ( \sqrt { 5 } - \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 5 } - \sqrt { 3 } - \sqrt { 2 } )$$

Baholash

$$114-38\sqrt{15}\approx -33,173367156$$

Yechim qadamlari

19 ga \sqrt{5}-\sqrt{3}+\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(19\sqrt{5}-19\sqrt{3}+19\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}-\sqrt{2}\right)$$

19\sqrt{5}-19\sqrt{3}+19\sqrt{2} ifodaning har bir elementini \sqrt{5}-\sqrt{3}-\sqrt{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$19\left(\sqrt{5}\right)^{2}-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$19\times 5-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

95 hosil qilish uchun 19 va 5 ni ko'paytirish.

$$95-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$95-19\sqrt{15}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{5} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{15}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

-38\sqrt{15} ni olish uchun -19\sqrt{15} va -19\sqrt{15} ni birlashtirish.

$$95-38\sqrt{15}-19\sqrt{10}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$95-38\sqrt{15}-19\sqrt{10}+19\times 3+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

57 hosil qilish uchun 19 va 3 ni ko'paytirish.

$$95-38\sqrt{15}-19\sqrt{10}+57+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

152 olish uchun 95 va 57'ni qo'shing.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{2} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{10}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

0 ni olish uchun -19\sqrt{10} va 19\sqrt{10} ni birlashtirish.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{6}-19\left(\sqrt{2}\right)^{2}$$

0 ni olish uchun 19\sqrt{6} va -19\sqrt{6} ni birlashtirish.

$$152-38\sqrt{15}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{2} kvadrati – 2.

$$152-38\sqrt{15}-19\times 2$$

-38 hosil qilish uchun -19 va 2 ni ko'paytirish.

$$152-38\sqrt{15}-38$$

114 olish uchun 152 dan 38 ni ayirish.

$$114-38\sqrt{15}$$