Đáp án:
Giải thích các bước giải:
$=(3-\sqrt[]{5})(\sqrt[]{\frac{6+2\sqrt[]{5}}{2}})+(3+\sqrt[]{5})(\sqrt[]{\frac{6-2\sqrt[]{5}}{2}})$
$=(3-\sqrt[]{5})\sqrt[]{\frac{5+2\sqrt[]{5}+1}{2}}+(3+\sqrt[]{5})\sqrt[]{\frac{5-2\sqrt[]{5}+1}{2}}$
$=(3-\sqrt[]{5})\sqrt[]{\frac{(\sqrt[]{5}+1)^{2}}{2}}+(3+\sqrt[]{5})\sqrt[]{\frac{(\sqrt[]{5}-1)^{2}}{2}}$
$=(3-\sqrt[]{5})\frac{(\sqrt[]{5}+1)}{\sqrt[]{2}}+(3+\sqrt[]{5})\frac{(\sqrt[]{5}-1)}{\sqrt[]{2}}$
$=\frac{((3-\sqrt[]{5})\sqrt[]{5}+(3+\sqrt[]{5})\sqrt[]{5})+((3-\sqrt[]{5})-(3+\sqrt[]{5}))}{\sqrt[]{2}}$
$=\frac{6\sqrt[]{5}-2\sqrt[]{5}}{\sqrt[]{2}}$
$=\frac{4\sqrt[]{5}}{\sqrt[]{2}}$
$=2\sqrt[]{10}$
