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nhin bai o tren se thay minh lam

Có: \(\frac{P}{\sqrt{2}}=\frac{1}{\sqrt{2}}\left(\frac{3+\sqrt{5}}{\sqrt{10}+\sqrt{3+\sqrt{5}}}-\frac{3-\sqrt{5}}{\sqrt{10}+\sqrt{3-\sqrt{5}}}\right)\)

\(=\frac{3+\sqrt{5}}{\sqrt{20}+\sqrt{6+2\sqrt{5}}}-\frac{3-\sqrt{5}}{\sqrt{20}+\sqrt{6-2\sqrt{5}}}\)

\(=\frac{3+\sqrt{5}}{\sqrt{20}+\sqrt{\left(\sqrt{5}+1\right)^2}}-\frac{3-\sqrt{5}}{\sqrt{20}+\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(=\frac{3+\sqrt{5}}{2\sqrt{5}+\sqrt{5}+1}-\frac{3-\sqrt{5}}{2\sqrt{5}+\sqrt{5}-1}\)

\(=\frac{3+\sqrt{5}}{3\sqrt{5}+1}-\frac{3-\sqrt{5}}{3\sqrt{5}-1}\)

\(=\frac{\left(3+\sqrt{5}\right)\left(3\sqrt{5}-1\right)-\left(3-\sqrt{5}\right)\left(3\sqrt{5}+1\right)}{\left(3\sqrt{5}+1\right)\left(3\sqrt{5}-1\right)}\)

\(=\frac{9\sqrt{5}-3+15-\sqrt{5}-9\sqrt{5}-3+15+\sqrt{5}}{9\cdot5-1}\)

\(=\frac{24}{44}=\frac{6}{11}\)

=>P=\(\frac{6}{11}\cdot\sqrt{2}=\frac{6\sqrt{2}}{11}\)

Chính xác 100% mink thử bằng máy tính r

mink làm hơi tắt phần nào k hiểu hói mink nhé

\(\sqrt{\frac{3\sqrt{5}+1}{2\sqrt{5}-3}}\left(\sqrt{10}-\sqrt{2}\right)\)

\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3+\sqrt{5}}\)

?? :v

\(\sqrt{\frac{3\sqrt{5}+1}{2\sqrt{5}-3}}\left(\sqrt{10}-\sqrt{2}\right)\)

\(=\sqrt{\frac{\left(3\sqrt{5}+1\right)\left(2\sqrt{5}+3\right)}{\left(2\sqrt{5}-3\right)\left(2\sqrt{5}+3\right)}}.\left(\sqrt{10}-\sqrt{2}\right)\)

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

\(=\sqrt{6+2\sqrt{5}}.\left(\sqrt{5}-1\right)\)

\(=\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)=4\)

\(\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}-\sqrt{5}}-\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}-\sqrt{5}}+\frac{\sqrt{3}-\sqrt{5}}{\sqrt{3}+\sqrt{5}}\)

\(=\frac{\left(\sqrt{3}+\sqrt{5}\right)^2+\left(\sqrt{3}-\sqrt{5}\right)^2}{\left(\sqrt{3}-\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}=\frac{3+2\sqrt{15}+5+3-2\sqrt{15}+5}{3-5}\)

\(=\frac{3+5+3+5}{-2}=\frac{16}{-2}=-8\)