1 Rút gọn\(B\)=\(\sqrt{x+\sqrt{2x-1}}\) + \(\sqrt{x-\sqrt{2x-1}}\)\(C\)=\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)2 tìm x thỏa mãn\(A=\sqrt{\frac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)Giúp mình...
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1 Rút gọn
\(B\)=\(\sqrt{x+\sqrt{2x-1}}\) + \(\sqrt{x-\sqrt{2x-1}}\)
\(C\)=\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
2 tìm x thỏa mãn
\(A=\sqrt{\frac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)
Giúp mình với
B1:
\(C=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
\(=\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)\)
\(=\sqrt{3^2-\left(\sqrt{5}\right)^2}\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)\)
\(=\sqrt{2}\left(\sqrt{3-\sqrt{5}}.\sqrt{2}+\sqrt{3+\sqrt{5}}.\sqrt{2}\right)\)
\(=\sqrt{2}\left(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\right)\)
\(=\sqrt{2}\left(\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}\right)\)
\(=\sqrt{2}\left(\sqrt{5}-1+\sqrt{5}+1\right)=2\sqrt{10}\)