Solucionar ((sqrt{2}-1+{left(2sqrt{2}-1right)}^2+2sqrt{2})

$$(( \sqrt{ 2 } -1+ { \left(2 \sqrt{ 2 } -1 \right) }^{ 2 } +2 \sqrt{ 2 } )$$

Calcular

$$8-\sqrt{2}\approx 6,585786438$$

Pasos de la solución

Utilice el teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(2\sqrt{2}-1\right)^{2}.

$$\sqrt{2}-1+4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1+2\sqrt{2}$$

El cuadrado de \sqrt{2} es 2.

$$\sqrt{2}-1+4\times 2-4\sqrt{2}+1+2\sqrt{2}$$

Multiplica 4 y 2 para obtener 8.

$$\sqrt{2}-1+8-4\sqrt{2}+1+2\sqrt{2}$$

Suma 8 y 1 para obtener 9.

$$\sqrt{2}-1+9-4\sqrt{2}+2\sqrt{2}$$

Suma -1 y 9 para obtener 8.

$$\sqrt{2}+8-4\sqrt{2}+2\sqrt{2}$$

Combina \sqrt{2} y -4\sqrt{2} para obtener -3\sqrt{2}.

$$-3\sqrt{2}+8+2\sqrt{2}$$

Combina -3\sqrt{2} y 2\sqrt{2} para obtener -\sqrt{2}.

$$-\sqrt{2}+8$$