[1/2(sqrt{5}+sqrt{3})]^2 eching

$$[ \frac { 1 } { 2 } ( \sqrt { 5 } + \sqrt { 3 } ) ] ^ { 2 }$$

Baholash

$$\frac{\sqrt{15}}{2}+2\approx 3,936491673$$

Yechim qadamlari

\frac{1}{2} ga \sqrt{5}+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\frac{5}{4} hosil qilish uchun \frac{1}{4} va 5 ni ko'paytirish.

$$\frac{5}{4}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

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

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3$$

\frac{3}{4} hosil qilish uchun \frac{1}{4} va 3 ni ko'paytirish.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}$$

2 olish uchun \frac{5}{4} va \frac{3}{4}'ni qo'shing.

$$2+\frac{1}{2}\sqrt{15}$$

Kengaytirish

$$\frac{\sqrt{15}}{2} + 2 = 3,936491673$$

Yechim qadamlari

\frac{1}{2} ga \sqrt{5}+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\frac{5}{4} hosil qilish uchun \frac{1}{4} va 5 ni ko'paytirish.

$$\frac{5}{4}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

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

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3$$

\frac{3}{4} hosil qilish uchun \frac{1}{4} va 3 ni ko'paytirish.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}$$

2 olish uchun \frac{5}{4} va \frac{3}{4}'ni qo'shing.

$$2+\frac{1}{2}\sqrt{15}$$