frac{sqrt{3}-1}{sqrt{3}+1}*frac{sqrt{3}+1}{sqrt{3}+1} eching

$$\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \times \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } + 1 }$$

Baholash

$$2-\sqrt{3}\approx 0,267949192$$

Yechim qadamlari

1 ni olish uchun \sqrt{3}+1 ni \sqrt{3}+1 ga bo‘ling.

$$\frac{\sqrt{3}-1}{\sqrt{3}+1}\times 1$$

\frac{\sqrt{3}-1}{\sqrt{3}+1} maxrajini \sqrt{3}-1 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\times 1$$

Hisoblang: \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}\times 1$$

\sqrt{3} kvadratini chiqarish. 1 kvadratini chiqarish.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{3-1}\times 1$$

2 olish uchun 3 dan 1 ni ayirish.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{2}\times 1$$

\left(\sqrt{3}-1\right)^{2} hosil qilish uchun \sqrt{3}-1 va \sqrt{3}-1 ni ko'paytirish.

$$\frac{\left(\sqrt{3}-1\right)^{2}}{2}\times 1$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{3}-1\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1}{2}\times 1$$

\sqrt{3} kvadrati – 3.

$$\frac{3-2\sqrt{3}+1}{2}\times 1$$

4 olish uchun 3 va 1'ni qo'shing.

$$\frac{4-2\sqrt{3}}{2}\times 1$$

2-\sqrt{3} natijani olish uchun 4-2\sqrt{3} ning har bir ifodasini 2 ga bo‘ling.

$$\left(2-\sqrt{3}\right)\times 1$$

2-\sqrt{3} ga 1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2-\sqrt{3}$$

Omil

$$2-\sqrt{3}$$