2/sqrt{7+sqrt{3}} eching

$$\frac{ 2 }{ \sqrt{ 7 } + \sqrt{ 3 } }$$

Baholash

$$\frac{\sqrt{7}-\sqrt{3}}{2}\approx 0,456850252$$

Yechim qadamlari

\frac{2}{\sqrt{7}+\sqrt{3}} maxrajini \sqrt{7}-\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\left(\sqrt{7}-\sqrt{3}\right)}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}$$

Hisoblang: \left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(\sqrt{7}-\sqrt{3}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

\sqrt{7} kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{2\left(\sqrt{7}-\sqrt{3}\right)}{7-3}$$

4 olish uchun 7 dan 3 ni ayirish.

$$\frac{2\left(\sqrt{7}-\sqrt{3}\right)}{4}$$

\frac{1}{2}\left(\sqrt{7}-\sqrt{3}\right) ni olish uchun 2\left(\sqrt{7}-\sqrt{3}\right) ni 4 ga bo‘ling.

$$\frac{1}{2}\left(\sqrt{7}-\sqrt{3}\right)$$

\frac{1}{2} ga \sqrt{7}-\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{2}\sqrt{7}+\frac{1}{2}\left(-1\right)\sqrt{3}$$

-\frac{1}{2} hosil qilish uchun \frac{1}{2} va -1 ni ko'paytirish.

$$\frac{1}{2}\sqrt{7}-\frac{1}{2}\sqrt{3}$$