Toán 9 rút gọn

Mộc Nhãn said:

[tex]2(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}})^2=[\sqrt{2}(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}})]^2=(\sqrt{4+2\sqrt{3}}+\sqrt{6-2\sqrt{5}})^2=[\sqrt{(\sqrt{3}+1)^2}+\sqrt{(\sqrt{5}-1)^2}]^2=(\sqrt{3}+1+\sqrt{5}-1)^2=(\sqrt{5}+\sqrt{3})^2=5+3+2\sqrt{15}=8+2\sqrt{15} \Rightarrow (\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}})^2=4+\sqrt{15}[/tex]
[tex]2(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}})^2=[\sqrt{2}(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}})]^2=(\sqrt{4-2\sqrt{3}}+\sqrt{6+2\sqrt{5}})^2=[\sqrt{(\sqrt{3}-1)^2}+\sqrt{(\sqrt{5}+1)^2}]^2=(\sqrt{3}-1+\sqrt{5}+1)^2=(\sqrt{5}+\sqrt{3})^2=5+3+2\sqrt{15}=8+2\sqrt{15} \Rightarrow (\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}})^2=4+\sqrt{15}[/tex]
Sau đó thay vào thôi.

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