Resolver frac{2left(0.8+sqrt{2}right)}{{left(0.2sqrt{2}-0.06right)}^2}

$$\frac{ 2 \left( 0.8+ \sqrt{ 2 } \right) }{ { \left(0.2 \sqrt{ 2 } -0.06 \right) }^{ 2 } }$$

Calcular

$$\frac{1285000\sqrt{2}+1436000}{36481}\approx 89.176953144$$

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(0.2\sqrt{2}-0.06\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\left(\sqrt{2}\right)^{2}-0.024\sqrt{2}+0.0036}$$

O cadrado de \sqrt{2} é 2.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\times 2-0.024\sqrt{2}+0.0036}$$

Multiplica 0.04 e 2 para obter 0.08.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.08-0.024\sqrt{2}+0.0036}$$

Suma 0.08 e 0.0036 para obter 0.0836.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}}$$

Racionaliza o denominador de \frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}} mediante a multiplicación do numerador e o denominador por 0.0836+0.024\sqrt{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{\left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}$$

Considera \left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.0836^{2}-\left(-0.024\sqrt{2}\right)^{2}}$$

Calcula 0.0836 á potencia de 2 e obtén 0.00698896.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\sqrt{2}\right)^{2}}$$

Expande \left(-0.024\sqrt{2}\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Calcula -0.024 á potencia de 2 e obtén 0.000576.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\left(\sqrt{2}\right)^{2}}$$

O cadrado de \sqrt{2} é 2.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\times 2}$$

Multiplica 0.000576 e 2 para obter 0.001152.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.001152}$$

Resta 0.001152 de 0.00698896 para obter 0.00583696.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00583696}$$

Divide 2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right) entre 0.00583696 para obter \frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right).

$$\frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Usa a propiedade distributiva para multiplicar \frac{12500000}{36481} por 0.8+\sqrt{2}.

$$\left(\frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Usa a propiedade distributiva para multiplicar \frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2} por 0.0836+0.024\sqrt{2} e combina os termos semellantes.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\left(\sqrt{2}\right)^{2}$$

O cadrado de \sqrt{2} é 2.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\times 2$$

Multiplica \frac{300000}{36481} e 2 para obter \frac{600000}{36481}.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{600000}{36481}$$

Suma \frac{836000}{36481} e \frac{600000}{36481} para obter \frac{1436000}{36481}.

$$\frac{1436000}{36481}+\frac{1285000}{36481}\sqrt{2}$$