Question

Area: Algebra Tema: Productos Notables I

Answer 1

Respuesta:

c) 20

Explicación paso a paso:

$M=\left(\sqrt{7}+\sqrt{3}\right)^2+\left(\sqrt{7}-\sqrt{3}\right)^2$

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$\left(\sqrt{7}+\sqrt{3}\right)^2\\=\left(\sqrt{7}\right)^2+2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^2\\\left(\sqrt{7}\right)^2=7\\2\sqrt{7}\sqrt{3}=2\sqrt{21}\\\left(\sqrt{3}\right)^2=3\\=7+2\sqrt{21}+3\\=10+2\sqrt{21}$

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$M=10+2\sqrt{21}+\left(\sqrt{7}-\sqrt{3}\right)^2$

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$\left(\sqrt{7}-\sqrt{3}\right)^2\\=\left(\sqrt{7}\right)^2-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^2\\\left(\sqrt{7}\right)^2=7\\2\sqrt{7}\sqrt{3}=2\sqrt{21}\\\left(\sqrt{3}\right)^2=3\\=7-2\sqrt{21}+3\\=10-2\sqrt{21}$

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$M=10+2\sqrt{21}+10-2\sqrt{21}\\2\sqrt{21}-2\sqrt{21}=0\\=10+10\\M=20$