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

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

Arvuta

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

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja 886731088897-627013566048\sqrt{2} nimetaja \frac{886731088897-627013566048\sqrt{2}}{886731088897+627013566048\sqrt{2}} nimetaja.

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

Mõelge valemile \left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Korrutage 886731088897-627013566048\sqrt{2} ja 886731088897-627013566048\sqrt{2}, et leida \left(886731088897-627013566048\sqrt{2}\right)^{2}.

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

Kasutage kaksliikme \left(886731088897-627013566048\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Korrutage 393146012008229658338304 ja 2, et leida 786292024016459316676608.

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

Liitke 786292024016459316676609 ja 786292024016459316676608, et leida 1572584048032918633353217.

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

Arvutage 2 aste 886731088897 ja leidke 786292024016459316676609.

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

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

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

Arvutage 2 aste 627013566048 ja leidke 393146012008229658338304.

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

\sqrt{2} ruut on 2.

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

Korrutage 393146012008229658338304 ja 2, et leida 786292024016459316676608.

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

Lahutage 786292024016459316676608 väärtusest 786292024016459316676609, et leida 1.

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

Arv jagatuna ühega annab tulemiks arvu enda.

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