Bài 1: Rút gọn
a, \(\sqrt{3}\) - \(\frac{1}{3}\sqrt{27}\) + \(2\sqrt{507}\)
b, (\(\sqrt{28}\)-\(\sqrt{12}\) -\(\sqrt{7}\) ) . \(\sqrt{7}\) + \(2\sqrt{21}\)
c, \(2\sqrt{40\sqrt{12}}\) - \(2\sqrt{\sqrt{75}}\) - \(3\sqrt{5\sqrt{48}}\)
Bài 2: Giải phương trình
a , \(5\sqrt{12x}\) - \(4\sqrt{3x}\) + \(2\sqrt{48x}\) = 14
b , \(\sqrt{4x-20}\) + \(\sqrt{x-5}\) - \(\frac{1}{3}\) \(\sqrt{9x-45}\) = 4
MONG CÁC ANH CHỊ GIÚP EM EM CẢM ƠN TRƯỚC ĐỪNG LÀM TẮT EM KHÓ HIỂU
Bài 1: (cái này là khai căn nên làm tắt xíu nha)
\(a.\sqrt{3}-\frac{1}{3}\sqrt{27}+2\sqrt{507}\\ =\sqrt{3}-\frac{1}{3}\sqrt{9\cdot3}+2\sqrt{169\cdot3}\\ =\sqrt{3}-\frac{1}{3}\cdot3\sqrt{3}+2\cdot13\sqrt{3}\\ =\sqrt{3}-\sqrt{3}+26\sqrt{3}=26\sqrt{3}\)
\(b.\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\cdot\sqrt{7}+2\sqrt{21}\\ =\left(\sqrt{4\cdot7}-\sqrt{4\cdot3}-\sqrt{7}\right)\cdot\sqrt{7}+2\sqrt{21}\\ =\left(2\sqrt{7}-2\sqrt{3}-\sqrt{7}\right)\cdot\sqrt{7}+2\sqrt{21}\\ =\left(\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\\ =\left(\sqrt{7}\right)^2-2\sqrt{21}+2\sqrt{21}=7\)
\(c.2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\\ =2\sqrt{40\sqrt{4\cdot3}}-2\sqrt{\sqrt{25\cdot3}}-3\sqrt{5\sqrt{16\cdot3}}\\ =2\sqrt{16\cdot5\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{5\cdot4\sqrt{3}}\\ =8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=0\)
Bài 2:
a. ĐKXĐ: \(x\ge0\)
\(5\sqrt{12x}-4\sqrt{3x}+2\sqrt{48x}=14\\ \Leftrightarrow5\sqrt{4\cdot3x}-4\sqrt{3x}+2\sqrt{16\cdot3x}=14\\ \Leftrightarrow10\sqrt{3x}-4\sqrt{3x}+8\sqrt{3x}=14\\ \Leftrightarrow14\sqrt{3x}=14\\ \Leftrightarrow\sqrt{3x}=1\\ \Leftrightarrow3x=1\Leftrightarrow x=\frac{1}{3}\left(tm\right)\)
b. ĐKXĐ: \(x\ge5\)
\(\sqrt{4x-20}+\sqrt{x-5}-\frac{1}{3}\sqrt{9x-45}=4\\ \Leftrightarrow\sqrt{4\left(x-5\right)}+\sqrt{x-5}-\frac{1}{3}\sqrt{9\left(x-5\right)}=4\\ \Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\\ \Leftrightarrow2\sqrt{x-5}=4\\ \Leftrightarrow\sqrt{x-5}=2\\ \Leftrightarrow x-5=4\Leftrightarrow x=9\left(tm\right)\)