Question

$(\sqrt{5}+3)^{2} +(4-\sqrt{5})^{2}+2\sqrt{5}$

Answer 1

Explicación paso a paso:

$(\sqrt{5}+3)^{2} +(4-\sqrt{5})^{2}+2\sqrt{5}$ ; aplicando los productos notables $(a+b)^{2}=(a)^{2}+2(a)(b)+(b)^{2}$ y $(a-b)^{2}=(a)^{2}-2(a)(b)+(b)^{2}$; lo anterior nos queda:

$(\sqrt{5}+3)^{2}=(\sqrt{5})^{2}+2(\sqrt{5})(3)+(3)^{2}=5+6\sqrt{5}+9=\\=14+6\sqrt{5}\\\\(4-\sqrt{5})^{2}=(4)^{2}-2(4)(\sqrt{5})+(\sqrt{5})^{2}=16-8\sqrt{5}+5=\\=21-8\sqrt{5}$; reuniendo todo y simplificando:

$(\sqrt{5}+3)^{2} +(4-\sqrt{5})^{2}+2\sqrt{5}=14+6\sqrt{5}+21-8\sqrt{5}+2\sqrt{5}=\\=14+21+6\sqrt{5}+2\sqrt{5}-8\sqrt{5}=\\=35+8\sqrt{5}-8\sqrt{5}=\boxed{35}$