frac{sqrt{6}-sqrt{2}}{4}*frac{sqrt{6}-1sqrt{2}}{4} eching

$$\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 } \times \frac { \sqrt { 6 } - 1 \sqrt { 2 } } { 4 }$$

Baholash

$$-\frac{\sqrt{3}}{4}+\frac{1}{2}\approx 0,066987298$$

Yechim qadamlari

\left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2} hosil qilish uchun \frac{\sqrt{6}-\sqrt{2}}{4} va \frac{\sqrt{6}-\sqrt{2}}{4} ni ko'paytirish.

$$\left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2}$$

\frac{\sqrt{6}-\sqrt{2}}{4}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(\sqrt{6}-\sqrt{2}\right)^{2}}{4^{2}}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{6}-\sqrt{2}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{6} kvadrati – 6.

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

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

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

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

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

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

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

\sqrt{2} kvadrati – 2.

$$\frac{6-4\sqrt{3}+2}{4^{2}}$$

8 olish uchun 6 va 2'ni qo'shing.

$$\frac{8-4\sqrt{3}}{4^{2}}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\frac{8-4\sqrt{3}}{16}$$

Omil

$$\frac{2 - \sqrt{3}}{4} = 0,0669872981077807$$