frac{7+sqrt{6}}{7-sqrt{6}}-frac{7-sqrt{6}}{7+sqrt{6}} eching

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

Baholash

$$\frac{28\sqrt{6}}{43}\approx 1,595016577$$

Qisqa yechim qadamlari

\frac{7+\sqrt{6}}{7-\sqrt{6}} maxrajini 7+\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{\left(7-\sqrt{6}\right)\left(7+\sqrt{6}\right)}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Hisoblang: \left(7-\sqrt{6}\right)\left(7+\sqrt{6}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

7 kvadratini chiqarish. \sqrt{6} kvadratini chiqarish.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{49-6}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

43 olish uchun 49 dan 6 ni ayirish.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

\left(7+\sqrt{6}\right)^{2} hosil qilish uchun 7+\sqrt{6} va 7+\sqrt{6} ni ko'paytirish.

$$\frac{\left(7+\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(7+\sqrt{6}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{49+14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

\sqrt{6} kvadrati – 6.

$$\frac{49+14\sqrt{6}+6}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

55 olish uchun 49 va 6'ni qo'shing.

$$\frac{55+14\sqrt{6}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

\frac{7-\sqrt{6}}{7+\sqrt{6}} maxrajini 7-\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{\left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right)}$$

Hisoblang: \left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}$$

7 kvadratini chiqarish. \sqrt{6} kvadratini chiqarish.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{49-6}$$

43 olish uchun 49 dan 6 ni ayirish.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{43}$$

\left(7-\sqrt{6}\right)^{2} hosil qilish uchun 7-\sqrt{6} va 7-\sqrt{6} ni ko'paytirish.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)^{2}}{43}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(7-\sqrt{6}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}$$

\sqrt{6} kvadrati – 6.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+6}{43}$$

55 olish uchun 49 va 6'ni qo'shing.

$$\frac{55+14\sqrt{6}}{43}-\frac{55-14\sqrt{6}}{43}$$

\frac{55+14\sqrt{6}}{43} va \frac{55-14\sqrt{6}}{43} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{55+14\sqrt{6}-\left(55-14\sqrt{6}\right)}{43}$$

55+14\sqrt{6}-\left(55-14\sqrt{6}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{55+14\sqrt{6}-55+14\sqrt{6}}{43}$$

55+14\sqrt{6}-55+14\sqrt{6} hisob-kitobini qiling.

$$\frac{28\sqrt{6}}{43}$$