sqrt{2}+1-frac{1+sqrt{2}}{sqrt{2}+156} eching

$$\sqrt{ 2 } +1- \frac{ 1+ \sqrt{ 2 } }{ \sqrt{ 2 } +156 }$$

Baholash

$$\frac{24179\sqrt{2}}{24334}+\frac{12090}{12167}\approx 2,398876869$$

Qisqa yechim qadamlari

\frac{1+\sqrt{2}}{\sqrt{2}+156} maxrajini \sqrt{2}-156 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}+156\right)\left(\sqrt{2}-156\right)}$$

Hisoblang: \left(\sqrt{2}+156\right)\left(\sqrt{2}-156\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}\right)^{2}-156^{2}}$$

\sqrt{2} kvadratini chiqarish. 156 kvadratini chiqarish.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{2-24336}$$

-24334 olish uchun 2 dan 24336 ni ayirish.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{-24334}$$

1+\sqrt{2} ifodaning har bir elementini \sqrt{2}-156 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+\left(\sqrt{2}\right)^{2}-156\sqrt{2}}{-24334}$$

\sqrt{2} kvadrati – 2.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+2-156\sqrt{2}}{-24334}$$

-154 olish uchun -156 va 2'ni qo'shing.

$$\sqrt{2}+1-\frac{\sqrt{2}-154-156\sqrt{2}}{-24334}$$

-155\sqrt{2} ni olish uchun \sqrt{2} va -156\sqrt{2} ni birlashtirish.

$$\sqrt{2}+1-\frac{-155\sqrt{2}-154}{-24334}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\sqrt{2}+1-\frac{155\sqrt{2}+154}{24334}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \sqrt{2}+1 ni \frac{24334}{24334} marotabaga ko'paytirish.

$$\frac{24334\left(\sqrt{2}+1\right)}{24334}-\frac{155\sqrt{2}+154}{24334}$$

\frac{24334\left(\sqrt{2}+1\right)}{24334} va \frac{155\sqrt{2}+154}{24334} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right)}{24334}$$

24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{24334\sqrt{2}[phone]\sqrt{2}-154}{24334}$$

24334\sqrt{2}[phone]\sqrt{2}-154 hisob-kitobini qiling.

$$\frac{24179\sqrt{2}+24180}{24334}$$