frac{sqrt{3}-sqrt{7}}{sqrt{3}+sqrt{7}} eching

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

Baholash

$$\frac{\sqrt{21}-5}{2}\approx -0,208712153$$

Yechim qadamlari

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

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

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

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

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

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

-4 olish uchun 3 dan 7 ni ayirish.

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

\left(\sqrt{3}-\sqrt{7}\right)^{2} hosil qilish uchun \sqrt{3}-\sqrt{7} va \sqrt{3}-\sqrt{7} ni ko'paytirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{3}-\sqrt{7}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{3} kvadrati – 3.

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

\sqrt{3} va \sqrt{7} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{3-2\sqrt{21}+\left(\sqrt{7}\right)^{2}}{-4}$$

\sqrt{7} kvadrati – 7.

$$\frac{3-2\sqrt{21}+7}{-4}$$

10 olish uchun 3 va 7'ni qo'shing.

$$\frac{10-2\sqrt{21}}{-4}$$