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Giải phương trình
a) \(\sqrt 2 .x – \sqrt {50} = 0\);
b) \(\sqrt 3 .x + \sqrt 3 = \sqrt {12} + \sqrt {27}\);
c) \(\sqrt 3 .{x^2} – \sqrt {12} = 0\);
d) \({{{x^2}} \over {\sqrt 5 }} – \sqrt {20} = 0\)
Hướng dẫn giải:
a) \(\sqrt{2}.x – \sqrt{50} = 0\)
\(\Leftrightarrow \sqrt{2}x=\sqrt{50}\)
\(\Leftrightarrow x=\frac{\sqrt{50}}{\sqrt{2}}=\sqrt{25}=5\)
b) \(\sqrt{3}.x + \sqrt{3} = \sqrt{12} + \sqrt{27}\)
\(\Leftrightarrow \sqrt{3}(x+1)=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\)
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\(\Leftrightarrow x+1=5\Leftrightarrow x=4\)
c) \(\sqrt{3}x^2-\sqrt{12}=0\)
\(\Leftrightarrow \sqrt{3}x^2=2\sqrt{3}\)
\(\Leftrightarrow x^2=2\)
\(\Leftrightarrow x=\pm 2\)
d) \(\frac{x^{2}}{\sqrt{5}}- \sqrt{20} = 0\)
\(\Leftrightarrow \frac{x^2}{\sqrt{5}}=\sqrt{20}\)
\(\Leftrightarrow x^2=\sqrt{20.5}=10\)
\(\Leftrightarrow x=\pm \sqrt{10}\)