Question

(3- √5) . √​(3+√5) + ( 3+ √5). √(3-√5)

Answer 1

căn bậc hai(3-căn bậc hai(5))*(căn bậc hai(5)+3)+(3-căn bậc hai(5))*căn bậc hai(căn bậc hai(5)+3)

Answer 2

\(=\dfrac{\left(3-\sqrt{5}\right)\cdot\sqrt{6+2\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{6-2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\left(3-\sqrt{5}\right)\cdot\left(\sqrt{5}+1\right)+\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)}{\sqrt{2}}\)

\(=\dfrac{3\sqrt{5}+3-5-\sqrt{5}+3\sqrt{5}-3+5-\sqrt{5}}{\sqrt{2}}\)

\(=\dfrac{4\sqrt{5}}{\sqrt{2}}=2\sqrt{10}\)