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

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

Avaliar

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

Passos Para a Resolução

Racionalize o denominador de \frac{886731088897-627013566048\sqrt{2}}{886731088897+627013566048\sqrt{2}} ao multiplicar o numerador e o denominador por 886731088897-627013566048\sqrt{2}.

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

Considere \left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right). A multiplicação pode ser transformada na diferença dos quadrados através da regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Multiplique 886731088897-627013566048\sqrt{2} e 886731088897-627013566048\sqrt{2} para obter \left(886731088897-627013566048\sqrt{2}\right)^{2}.

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

Utilize o teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(886731088897-627013566048\sqrt{2}\right)^{2}.

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

O quadrado de \sqrt{2} é 2.

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

Multiplique 393146012008229658338304 e 2 para obter 786292024016459316676608.

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

Some 786292024016459316676609 e 786292024016459316676608 para obter 1572584048032918633353217.

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

Calcule 886731088897 elevado a 2 e obtenha 786292024016459316676609.

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

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

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

Calcule 627013566048 elevado a 2 e obtenha 393146012008229658338304.

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

O quadrado de \sqrt{2} é 2.

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

Multiplique 393146012008229658338304 e 2 para obter 786292024016459316676608.

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

Subtraia 786292024016459316676608 de 786292024016459316676609 para obter 1.

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

Qualquer número dividido por um resulta no próprio número.

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