Resol 19*(sqrt{5}-sqrt{3}+sqrt{2})(sqrt{5}-sqrt{3}-sqrt{2})

$$19 \cdot ( \sqrt { 5 } - \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 5 } - \sqrt { 3 } - \sqrt { 2 } )$$

Calcula

$$114-38\sqrt{15}\approx -33,173367156$$

Passos de solució

Utilitzeu la propietat distributiva per multiplicar 19 per \sqrt{5}-\sqrt{3}+\sqrt{2}.

$$\left(19\sqrt{5}-19\sqrt{3}+19\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}-\sqrt{2}\right)$$

Per aplicar la propietat distributiva, cal multiplicar cada terme de l'operació 19\sqrt{5}-19\sqrt{3}+19\sqrt{2} per cada terme de l'operació \sqrt{5}-\sqrt{3}-\sqrt{2}.

$$19\left(\sqrt{5}\right)^{2}-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

L'arrel quadrada de \sqrt{5} és 5.

$$19\times 5-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Multipliqueu 19 per 5 per obtenir 95.

$$95-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{3} i \sqrt{5}, Multipliqueu els números sota l'arrel quadrada.

$$95-19\sqrt{15}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{5} i \sqrt{2}, Multipliqueu els números sota l'arrel quadrada.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{3} i \sqrt{5}, Multipliqueu els números sota l'arrel quadrada.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{15}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Combineu -19\sqrt{15} i -19\sqrt{15} per obtenir -38\sqrt{15}.

$$95-38\sqrt{15}-19\sqrt{10}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

L'arrel quadrada de \sqrt{3} és 3.

$$95-38\sqrt{15}-19\sqrt{10}+19\times 3+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Multipliqueu 19 per 3 per obtenir 57.

$$95-38\sqrt{15}-19\sqrt{10}+57+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Sumeu 95 més 57 per obtenir 152.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{3} i \sqrt{2}, Multipliqueu els números sota l'arrel quadrada.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{2} i \sqrt{5}, Multipliqueu els números sota l'arrel quadrada.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{10}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Combineu -19\sqrt{10} i 19\sqrt{10} per obtenir 0.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Per multiplicar \sqrt{3} i \sqrt{2}, Multipliqueu els números sota l'arrel quadrada.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{6}-19\left(\sqrt{2}\right)^{2}$$

Combineu 19\sqrt{6} i -19\sqrt{6} per obtenir 0.

$$152-38\sqrt{15}-19\left(\sqrt{2}\right)^{2}$$

L'arrel quadrada de \sqrt{2} és 2.

$$152-38\sqrt{15}-19\times 2$$

Multipliqueu -19 per 2 per obtenir -38.

$$152-38\sqrt{15}-38$$

Resteu 152 de 38 per obtenir 114.

$$114-38\sqrt{15}$$