Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
\sqrt {9x + 27} - \frac{1}{2}\sqrt {4x + 12} + \sqrt {x + 3} = 6\\
dk:x \ge - 3\\
\Leftrightarrow 3\sqrt {x + 3} - \frac{1}{2}.2\sqrt {x + 3} + \sqrt {x + 3} = 6\\
\Leftrightarrow 3\sqrt {x + 3} - \sqrt {x + 3} + \sqrt {x + 3} = 6\\
\Leftrightarrow 3\sqrt {x + 3} = 6\\
\Leftrightarrow \sqrt {x + 3} = 2\\
\Leftrightarrow x + 3 = 4\\
\Leftrightarrow x = 1\left( {tm} \right)\\
vay:x = 1\\
2 + \sqrt {2x - 1} = 3\\
dk:x \ge \frac{1}{2}\\
\Leftrightarrow \sqrt {2x - 1} = 1\\
\Leftrightarrow 2x - 1 = 1\\
\Leftrightarrow 2x = 2\\
\Leftrightarrow x = 1\left( {tm} \right)\\
vay:x = 1\\
\sqrt {x + 4} - \sqrt {{x^2} - 16} = 0\\
dk:x \ge 4\\
\Leftrightarrow \sqrt {x + 4} - \sqrt {\left( {x - 4} \right)\left( {x + 4} \right)} = 0\\
\Leftrightarrow \sqrt {x + 4} \left( {1 - \sqrt {x - 4} } \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt {x + 4} = 0\\
1 - \sqrt {x - 4} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x + 4 = 0\\
x - 4 = 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 4\left( {ktm} \right)\\
x = 5\left( {tm} \right)
\end{array} \right.\\
vay:x = 5
\end{array}\]

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Answer 2

\[\begin{array}{l}
\sqrt {9x + 27} - \frac{1}{2}\sqrt {4x + 12} + \sqrt {x + 3} = 6\\
dk:x \ge - 3\\
\Leftrightarrow 3\sqrt {x + 3} - \frac{1}{2}.2\sqrt {x + 3} + \sqrt {x + 3} = 6\\
\Leftrightarrow 3\sqrt {x + 3} - \sqrt {x + 3} + \sqrt {x + 3} = 6\\
\Leftrightarrow 3\sqrt {x + 3} = 6\\
\Leftrightarrow \sqrt {x + 3} = 2\\
\Leftrightarrow x + 3 = 4\\
\Leftrightarrow x = 1\left( {tm} \right)\\
vay:x = 1\\
2 + \sqrt {2x - 1} = 3\\
dk:x \ge \frac{1}{2}\\
\Leftrightarrow \sqrt {2x - 1} = 1\\
\Leftrightarrow 2x - 1 = 1\\
\Leftrightarrow 2x = 2\\
\Leftrightarrow x = 1\left( {tm} \right)\\
vay:x = 1\\
\sqrt {x + 4} - \sqrt {{x^2} - 16} = 0\\
dk:x \ge 4\\
\Leftrightarrow \sqrt {x + 4} - \sqrt {\left( {x - 4} \right)\left( {x + 4} \right)} = 0\\
\Leftrightarrow \sqrt {x + 4} \left( {1 - \sqrt {x - 4} } \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt {x + 4} = 0\\
1 - \sqrt {x - 4} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x + 4 = 0\\
x - 4 = 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 4\left( {ktm} \right)\\
x = 5\left( {tm} \right)
\end{array} \right.\\
vay:x = 5
\end{array}\]

Answer 3

$\sqrt{9 x + 27} - \frac{1}{2} \sqrt{4 x + 12} + \sqrt{x + 3} = 6, đ k : x \geq - 3 < = > \sqrt{9 . (x + 3)} - \frac{1}{2} . \sqrt{4 . (x + 3)} + \sqrt{x + 3} = 6 < = > 3 \sqrt{x + 3} - \sqrt{x + 3} + \sqrt{x + 3} = 6 < = > 3 \sqrt{x + 3} = 6 < = > \sqrt{x + 3} = 2 < = > x + 3 = 4 < = > x = 1 (t m) V â y x = 1 2 + \sqrt{2 x - 1} = 3, đ k : x \geq \frac{1}{2} < = > \sqrt{2 x + 1} = 1 < = > 2 x + 1 = 1 < = > 2 x = 0 < = > x = 0 (l o ạ i) V ậ y x = \emptyset \sqrt{x + 4} - \sqrt{x^{2} - 16} = 0, đ k : x \geq 4 h o ặ c x = - 4$

$x = - 4 < = > 0 = 0 (đ ú n g) = > x = - 4 l à n g h ệ m x \neq - 4 t a c ó : \sqrt{x + 4} - \sqrt{(x + 4) (x - 4)} = 0 < = > 1 - \sqrt{x - 4} = 0 < = > \sqrt{x - 4} = 1 < = > x - 4 = 1 < = > x = 5 (t m) V ậ y S = \{- 4; 5\}$ .

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Answer 4

$\sqrt{9 x + 27} - \frac{1}{2} \sqrt{4 x + 12} + \sqrt{x + 3} = 6, đ k : x \geq - 3 < = > \sqrt{9 . (x + 3)} - \frac{1}{2} . \sqrt{4 . (x + 3)} + \sqrt{x + 3} = 6 < = > 3 \sqrt{x + 3} - \sqrt{x + 3} + \sqrt{x + 3} = 6 < = > 3 \sqrt{x + 3} = 6 < = > \sqrt{x + 3} = 2 < = > x + 3 = 4 < = > x = 1 (t m) V â y x = 1 2 + \sqrt{2 x - 1} = 3, đ k : x \geq \frac{1}{2} < = > \sqrt{2 x + 1} = 1 < = > 2 x + 1 = 1 < = > 2 x = 0 < = > x = 0 (l o ạ i) V ậ y x = \emptyset \sqrt{x + 4} - \sqrt{x^{2} - 16} = 0, đ k : x \geq 4 h o ặ c x = - 4$

$x = - 4 < = > 0 = 0 (đ ú n g) = > x = - 4 l à n g h ệ m x \neq - 4 t a c ó : \sqrt{x + 4} - \sqrt{(x + 4) (x - 4)} = 0 < = > 1 - \sqrt{x - 4} = 0 < = > \sqrt{x - 4} = 1 < = > x - 4 = 1 < = > x = 5 (t m) V ậ y S = \{- 4; 5\}$ .

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