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

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

Ovrednoti

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

Koraki rešitve

Racionalizirajte imenovalec \frac{886731088897-627013566048\sqrt{2}}{886731088897+627013566048\sqrt{2}} tako, da pomnožite števec in imenovalec s 886731088897-627013566048\sqrt{2}.

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

Razmislite o \left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Pomnožite 886731088897-627013566048\sqrt{2} in 886731088897-627013566048\sqrt{2}, da dobite \left(886731088897-627013566048\sqrt{2}\right)^{2}.

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

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(886731088897-627013566048\sqrt{2}\right)^{2}.

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

Kvadrat vrednosti \sqrt{2} je 2.

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

Pomnožite 393146012008229658338304 in 2, da dobite 786292024016459316676608.

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

Seštejte 786292024016459316676609 in 786292024016459316676608, da dobite 1572584048032918633353217.

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

Izračunajte potenco 886731088897 števila 2, da dobite 786292024016459316676609.

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

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

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

Izračunajte potenco 627013566048 števila 2, da dobite 393146012008229658338304.

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

Kvadrat vrednosti \sqrt{2} je 2.

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

Pomnožite 393146012008229658338304 in 2, da dobite 786292024016459316676608.

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

Odštejte 786292024016459316676608 od 786292024016459316676609, da dobite 1.

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

Če poljubno število delite z ena, dobite isto število.

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