1/-2-sqrt{2}+1/-2+sqrt{2} eching

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

Baholash

$$-2$$

Qisqa yechim qadamlari

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

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

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

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

-2 kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

$$\frac{-2+\sqrt{2}}{4-2}+\frac{1}{-2+\sqrt{2}}$$

2 olish uchun 4 dan 2 ni ayirish.

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

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

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

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

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

-2 kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

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

2 olish uchun 4 dan 2 ni ayirish.

$$\frac{-2+\sqrt{2}}{2}+\frac{-2-\sqrt{2}}{2}$$

\frac{-2+\sqrt{2}}{2} va \frac{-2-\sqrt{2}}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-2+\sqrt{2}-2-\sqrt{2}}{2}$$

-2+\sqrt{2}-2-\sqrt{2} hisob-kitobini qiling.

$$\frac{-4}{2}$$

-2 ni olish uchun -4 ni 2 ga bo‘ling.

$$-2$$

Omil

$$-2$$