frac{sqrt{4}-sqrt{3}}{sqrt{7}+sqrt{3}}+frac{sqrt{4}+sqrt{3}}{sqrt{7}-sqrt{3}} eching

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

Baholash

$$\sqrt{7}+\frac{3}{2}\approx 4,145751311$$

Qisqa yechim qadamlari

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

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

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

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

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}.

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

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

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

4 olish uchun 7 dan 3 ni ayirish.

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

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

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

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

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

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}.

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

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

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

4 olish uchun 7 dan 3 ni ayirish.

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

\frac{\left(2-\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}{4} va \frac{\left(2+\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(2-\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)+\left(2+\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right) ichidagi ko‘paytirishlarni bajaring.

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

2\sqrt{7}-2\sqrt{3}-\sqrt{21}+3+2\sqrt{7}+2\sqrt{3}+\sqrt{21}+3 hisob-kitobini qiling.

$$\frac{4\sqrt{7}+6}{4}$$