(1/2sqrt{3}-4sqrt{5})^2= eching

$$( \frac { 1 } { 2 } \sqrt { 3 } - 4 \sqrt { 5 } ) ^ { 2 } =$$

Baholash

$$\frac{323}{4}-4\sqrt{15}\approx 65,258066615$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

80 hosil qilish uchun 16 va 5 ni ko'paytirish.

$$\frac{3}{4}-4\sqrt{15}+80$$

\frac{323}{4} olish uchun \frac{3}{4} va 80'ni qo'shing.

$$\frac{323}{4}-4\sqrt{15}$$

Kengaytirish

$$\frac{323}{4} - 4 \sqrt{15} = 65,258066615$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

80 hosil qilish uchun 16 va 5 ni ko'paytirish.

$$\frac{3}{4}-4\sqrt{15}+80$$

\frac{323}{4} olish uchun \frac{3}{4} va 80'ni qo'shing.

$$\frac{323}{4}-4\sqrt{15}$$