Resolver 50^2+[25(sqrt{6}-sqrt{2})]^2-2*50*2(sqrt{6}-sqrt{2})*(633)^2

$$50 ^ { 2 } + [ 25 ( \sqrt { 6 } - \sqrt { 2 } ) ] ^ { 2 } - 2 \times 50 \times 2 ( \sqrt { 6 } - \sqrt { 2 } ) \times ( 633 ) ^ { 2 }$$

Calcular

$$80137800\sqrt{2}[phone]\sqrt{3}-80137800\sqrt{6}\approx -82961585.617486045$$

Pasos da solución

Calcula 50 á potencia de 2 e obtén 2500.

$$2500+\left(25\left(\sqrt{6}-\sqrt{2}\right)\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Usa a propiedade distributiva para multiplicar 25 por \sqrt{6}-\sqrt{2}.

$$2500+\left(25\sqrt{6}-25\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(25\sqrt{6}-25\sqrt{2}\right)^{2}.

$$2500+625\left(\sqrt{6}\right)^{2}-1250\sqrt{6}\sqrt{2}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

O cadrado de \sqrt{6} é 6.

$$2500+625\times 6-1250\sqrt{6}\sqrt{2}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica 625 e 6 para obter 3750.

$$2500+3750-1250\sqrt{6}\sqrt{2}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Factoriza 6=2\times 3. Reescribe a raíz cadrada do produto \sqrt{2\times 3} como o produto de raíces cadradas \sqrt{2}\sqrt{3}.

$$2500+3750-1250\sqrt{2}\sqrt{3}\sqrt{2}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica \sqrt{2} e \sqrt{2} para obter 2.

$$2500+3750-1250\times 2\sqrt{3}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica -1250 e 2 para obter -2500.

$$2500+3750-2500\sqrt{3}+625\left(\sqrt{2}\right)^{2}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

O cadrado de \sqrt{2} é 2.

$$2500+3750-2500\sqrt{3}+625\times 2-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica 625 e 2 para obter 1250.

$$2500+3750-2500\sqrt{3}+1250-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Suma 3750 e 1250 para obter 5000.

$$2500+5000-2500\sqrt{3}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Suma 2500 e 5000 para obter 7500.

$$7500-2500\sqrt{3}-2\times 2\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica 2 e 2 para obter 4.

$$7500-2500\sqrt{3}-4\times 50\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Multiplica 4 e 50 para obter 200.

$$7500-2500\sqrt{3}-200\left(\sqrt{6}-\sqrt{2}\right)\times 633^{2}$$

Calcula 633 á potencia de 2 e obtén 400689.

$$7500-2500\sqrt{3}-200\left(\sqrt{6}-\sqrt{2}\right)\times 400689$$

Multiplica 200 e 400689 para obter 80137800.

$$7500-2500\sqrt{3}-80137800\left(\sqrt{6}-\sqrt{2}\right)$$

Usa a propiedade distributiva para multiplicar -80137800 por \sqrt{6}-\sqrt{2}.

$$7500-2500\sqrt{3}-80137800\sqrt{6}[phone]\sqrt{2}$$

Factorizar

$$100 {(801378 \sqrt{2} + 75 - 25 \sqrt{3} - 801378 \sqrt{6})} = -82961585.61748604$$