frac{20^2+{left(20sqrt{2}right)}^2-400}{2*20*20sqrt{2}} eching

$$\frac{ { 20 }^{ 2 } + { \left(20 \sqrt{ 2 } \right) }^{ 2 } -400 }{ 2 \times 20 \times 20 \sqrt{ 2 } }$$

Baholash

$$\frac{\sqrt{2}}{2}\approx 0,707106781$$

Yechim qadamlari

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$\frac{400+\left(20\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

\left(20\sqrt{2}\right)^{2} ni kengaytirish.

$$\frac{400+20^{2}\left(\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$\frac{400+400\left(\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{400+400\times 2-400}{2\times 20\times 20\sqrt{2}}$$

800 hosil qilish uchun 400 va 2 ni ko'paytirish.

$$\frac{400+800-400}{2\times 20\times 20\sqrt{2}}$$

1200 olish uchun 400 va 800'ni qo'shing.

$$\frac{1200-400}{2\times 20\times 20\sqrt{2}}$$

800 olish uchun 1200 dan 400 ni ayirish.

$$\frac{800}{2\times 20\times 20\sqrt{2}}$$

40 hosil qilish uchun 2 va 20 ni ko'paytirish.

$$\frac{800}{40\times 20\sqrt{2}}$$

800 hosil qilish uchun 40 va 20 ni ko'paytirish.

$$\frac{800}{800\sqrt{2}}$$

\frac{800}{800\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{800\sqrt{2}}{800\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{800\sqrt{2}}{800\times 2}$$

Surat va maxrajdagi ikkala 800 ni qisqartiring.

$$\frac{\sqrt{2}}{2}$$