frac{sqrt{14}+2}{1-sqrt{7}} eching

$$\frac{ \sqrt{ 14 } +2 }{ 1- \sqrt{ 7 } }$$

Baholash

$$-\frac{\sqrt{7}}{3}-\frac{\sqrt{14}}{6}-\frac{7\sqrt{2}}{6}-\frac{1}{3}\approx -3,488775824$$

Yechim qadamlari

\frac{\sqrt{14}+2}{1-\sqrt{7}} maxrajini 1+\sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{\left(1-\sqrt{7}\right)\left(1+\sqrt{7}\right)}$$

Hisoblang: \left(1-\sqrt{7}\right)\left(1+\sqrt{7}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{1^{2}-\left(\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{1-7}$$

-6 olish uchun 1 dan 7 ni ayirish.

$$\frac{\left(\sqrt{14}+2\right)\left(1+\sqrt{7}\right)}{-6}$$

\sqrt{14}+2 ifodaning har bir elementini 1+\sqrt{7} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\sqrt{14}+\sqrt{14}\sqrt{7}+2+2\sqrt{7}}{-6}$$

Faktor: 14=7\times 2. \sqrt{7\times 2} koʻpaytmasining kvadrat ildizini \sqrt{7}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\sqrt{14}+\sqrt{7}\sqrt{2}\sqrt{7}+2+2\sqrt{7}}{-6}$$

7 hosil qilish uchun \sqrt{7} va \sqrt{7} ni ko'paytirish.

$$\frac{\sqrt{14}+7\sqrt{2}+2+2\sqrt{7}}{-6}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-\sqrt{14}-7\sqrt{2}-2-2\sqrt{7}}{6}$$