frac{1/sqrt{2}-1}{1/sqrt{2}+sqrt{3}} eching

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

Baholash

$$\frac{\sqrt{2}+\sqrt{6}-2\sqrt{3}-1}{5}\approx -0,120079662$$

Qisqa yechim qadamlari

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

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

\sqrt{2} kvadrati – 2.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{2}{2} marotabaga ko'paytirish.

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

\frac{\sqrt{2}}{2} va \frac{2}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

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

\sqrt{2} kvadrati – 2.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \sqrt{3} ni \frac{2}{2} marotabaga ko'paytirish.

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

\frac{\sqrt{2}}{2} va \frac{2\sqrt{3}}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\frac{\sqrt{2}-2}{2} ni \frac{\sqrt{2}+2\sqrt{3}}{2} ga bo'lish \frac{\sqrt{2}-2}{2} ga k'paytirish \frac{\sqrt{2}+2\sqrt{3}}{2} ga qaytarish.

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

Surat va maxrajdagi ikkala 2 ni qisqartiring.

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

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

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

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

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

\sqrt{2} kvadrati – 2.

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

\left(2\sqrt{3}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

\sqrt{3} kvadrati – 3.

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

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{2-12}$$

-10 olish uchun 2 dan 12 ni ayirish.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{-10}$$

\sqrt{2}-2 ifodaning har bir elementini \sqrt{2}-2\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

\sqrt{2} kvadrati – 2.

$$\frac{2-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{2-2\sqrt{6}-2\sqrt{2}+4\sqrt{3}}{-10}$$