\(a,\sqrt{4-\sqrt{10+2\sqrt{5}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}\\ =\sqrt{\left(\sqrt{4-\sqrt{10+2\sqrt{5}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}\right)^2}\\ =\sqrt{4-\sqrt{10+2\sqrt{5}}+2\sqrt{\left(4-\sqrt{10+2\sqrt{5}}\right)\left(4+\sqrt{10+2\sqrt{5}}\right)}+4+\sqrt{10+2\sqrt{5}}}\\ =\sqrt{8+2\sqrt{4^2-\left(\sqrt{10+2\sqrt{5}}\right)^2}}\\ =\sqrt{8+2\sqrt{16-10-2\sqrt{5}}}\\ =\sqrt{8+2\sqrt{6-2\sqrt{5}}}\\ =\sqrt{8+2\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1^2}}\\ =\sqrt{8+2\sqrt{\left(\sqrt{5}-1\right)^2}}\\ =\sqrt{8+2\sqrt{5}-2}\\ =\sqrt{6+2\sqrt{5}}\\ =\sqrt{\left(\sqrt{5}\right)^2+2\cdot\sqrt{5}\cdot1+1^2}\\ =\sqrt{5}+1\)
\(b,\left(2+\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\left(\sqrt{10}-\sqrt{2}\right)\\ =\left(2+\sqrt{4+\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1^2}}\right)\left(\sqrt{10}-\sqrt{2}\right)\\ =\left(2+\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\right)\left(\sqrt{10}-\sqrt{2}\right)\\ =\left(2+\sqrt{4+\sqrt{5}-1}\right)\cdot\sqrt{2}\cdot\left(\sqrt{5}-1\right)\\ =\left(2\sqrt{2}+\sqrt{8+2\sqrt{5}-2}\right)\left(\sqrt{5}-1\right)\\ =\left(2\sqrt{2}+\sqrt{6+2\sqrt{5}}\right)\left(\sqrt{5}-1\right)\\ =\left(2\sqrt{2}+\sqrt{\left(\sqrt{5}\right)^2+2\cdot\sqrt{5}\cdot1+1^2}\right)\left(\sqrt{5}-1\right)\\ =\left(2\sqrt{2}+\sqrt{\left(\sqrt{5}+1\right)^2}\right)\left(\sqrt{5}-1\right)\\ =\left(2\sqrt{2}+\sqrt{5}+1\right)\left(\sqrt{5}-1\right)\\ =2\sqrt{10}-2\sqrt{2}+5-\sqrt{5}+\sqrt{5}-1\\ =2\sqrt{10}-2\sqrt{2}+4\)
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