frac{886731088897-627013566048sqrt{2}}{886731088897+627013566048sqrt{2}} eching

$$\frac{ 886731088897-627013566048 \sqrt{ 2 } }{ 886731088897+627013566048 \sqrt{ 2 } }$$

Baholash

$$1572584048032918633353217-1111984844349868137938112\sqrt{2}\approx -268435456$$

Yechim qadamlari

\frac{886731088897-627013566048\sqrt{2}}{886731088897+627013566048\sqrt{2}} maxrajini 886731088897-627013566048\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}{\left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}$$

Hisoblang: \left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

\left(886731088897-627013566048\sqrt{2}\right)^{2} hosil qilish uchun 886731088897-627013566048\sqrt{2} va 886731088897-627013566048\sqrt{2} ni ko'paytirish.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)^{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(886731088897-627013566048\sqrt{2}\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+393146012008229658338304\left(\sqrt{2}\right)^{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+393146012008229658338304\times 2}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

786292024016459316676608 hosil qilish uchun 393146012008229658338304 va 2 ni ko'paytirish.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+786292024016459316676608}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

1572584048032918633353217 olish uchun 786292024016459316676609 va 786292024016459316676608'ni qo'shing.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 886731088897 ga hisoblang va 786292024016459316676609 ni qiymatni oling.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-\left(627013566048\sqrt{2}\right)^{2}}$$

\left(627013566048\sqrt{2}\right)^{2} ni kengaytirish.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-627013566048^{2}\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 627013566048 ga hisoblang va 393146012008229658338304 ni qiymatni oling.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-393146012008229658338304\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-393146012008229658338304\times 2}$$

786292024016459316676608 hosil qilish uchun 393146012008229658338304 va 2 ni ko'paytirish.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-786292024016459316676608}$$

1 olish uchun 786292024016459316676609 dan 786292024016459316676608 ni ayirish.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$1572584048032918633353217-1111984844349868137938112\sqrt{2}$$