Đáp án:
\(\begin{array}{l}
a,\\
x = 4\\
b,\\
x = - 28\\
c,\\
y = 9\\
d,\\
y = 28\\
e,\\
x = 9\\
f,\\
x = 15
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a,\\
DKXD:\,\,\,x \ge 0\\
\sqrt {16x} = 8\\
\Leftrightarrow \sqrt {{4^2}.x} = 8\\
\Leftrightarrow 4\sqrt x = 8\\
\Leftrightarrow \sqrt x = 2\\
\Leftrightarrow x = {2^2}\\
\Leftrightarrow x = 4\\
b,\\
DKXD:\,\,\,4 - 5x \ge 0 \Leftrightarrow x \le \dfrac{4}{5}\\
\sqrt {4 - 5x} = 12\\
\Leftrightarrow 4 - 5x = {12^2}\\
\Leftrightarrow 4 - 5x = 144\\
\Leftrightarrow 5x = 4 - 144\\
\Leftrightarrow 5x = - 140\\
\Leftrightarrow x = - 28\\
c,\\
DKXD:\,\,\,\,y \ge 5\\
\sqrt {4y - 20} + \sqrt {y - 5} - \dfrac{1}{3}\sqrt {9y - 45} = 4\\
\Leftrightarrow \sqrt {4.\left( {y - 5} \right)} + \sqrt {y - 5} - \dfrac{1}{3}\sqrt {9.\left( {y - 5} \right)} = 4\\
\Leftrightarrow \sqrt {{2^2}\left( {y - 5} \right)} + \sqrt {y - 5} - \dfrac{1}{3}\sqrt {{3^2}.\left( {y - 5} \right)} = 4\\
\Leftrightarrow 2.\sqrt {y - 5} + \sqrt {y - 5} - \dfrac{1}{3}.3\sqrt {y - 5} = 4\\
\Leftrightarrow 2.\sqrt {y - 5} + \sqrt {y - 5} - \sqrt {y - 5} = 4\\
\Leftrightarrow 2.\sqrt {y - 5} = 4\\
\Leftrightarrow \sqrt {y - 5} = 2\\
\Leftrightarrow y - 5 = {2^2}\\
\Leftrightarrow y - 5 = 4\\
\Leftrightarrow y = 9\\
d,\\
DKXD:\,\,\,y \ge 3\\
2\sqrt {9y - 27} - \dfrac{1}{5}\sqrt {25y - 75} - \dfrac{1}{7}\sqrt {49y - 147} = 20\\
\Leftrightarrow 2.\sqrt {9\left( {y - 3} \right)} - \dfrac{1}{5}\sqrt {25\left( {y - 3} \right)} - \dfrac{1}{7}\sqrt {49\left( {y - 3} \right)} = 20\\
\Leftrightarrow 2.\sqrt {{3^2}.\left( {y - 3} \right)} - \dfrac{1}{5}\sqrt {{5^2}.\left( {y - 3} \right)} - \dfrac{1}{7}\sqrt {{7^2}.\left( {y - 3} \right)} = 20\\
\Leftrightarrow 2.3\sqrt {y - 3} - \dfrac{1}{5}.5\sqrt {y - 3} - \dfrac{1}{7}.7\sqrt {y - 3} = 20\\
\Leftrightarrow 6\sqrt {y - 3} - \sqrt {y - 3} - \sqrt {y - 3} = 20\\
\Leftrightarrow 4.\sqrt {y - 3} = 20\\
\Leftrightarrow \sqrt {y - 3} = 5\\
\Leftrightarrow y - 3 = {5^2}\\
\Leftrightarrow y - 3 = 25\\
\Leftrightarrow y = 28\\
e,\\
DKXD:\,\,\,\,x \ge 5\\
\sqrt {4x - 20} - \dfrac{1}{3}\sqrt {9x - 45} + \sqrt {x - 5} = 4\\
\Leftrightarrow \sqrt {4.\left( {x - 5} \right)} - \dfrac{1}{3}\sqrt {9\left( {x - 5} \right)} + \sqrt {x - 5} = 4\\
\Leftrightarrow \sqrt {{2^2}\left( {x - 5} \right)} - \dfrac{1}{3}\sqrt {{3^2}\left( {x - 5} \right)} + \sqrt {x - 5} = 4\\
\Leftrightarrow 2\sqrt {x - 5} - \dfrac{1}{3}.3\sqrt {x - 5} + \sqrt {x - 5} = 4\\
\Leftrightarrow 2\sqrt {x - 5} - \sqrt {x - 5} + \sqrt {x - 5} = 4\\
\Leftrightarrow 2\sqrt {x - 5} = 4\\
\Leftrightarrow \sqrt {x - 5} = 2\\
\Leftrightarrow x - 5 = {2^2}\\
\Leftrightarrow x - 5 = 4\\
\Leftrightarrow x = 9\\
f,\\
DKXD:\,\,\,x \ge - 1\\
\sqrt {16x + 16} - \sqrt {9x + 9} + \sqrt {4x + 4} = 16 - \sqrt {x + 1} \\
\Leftrightarrow \sqrt {16\left( {x + 1} \right)} - \sqrt {9\left( {x + 1} \right)} + \sqrt {4\left( {x + 1} \right)} = 16 - \sqrt {x + 1} \\
\Leftrightarrow \sqrt {{4^2}.\left( {x + 1} \right)} - \sqrt {{3^2}.\left( {x + 1} \right)} + \sqrt {{2^2}.\left( {x + 1} \right)} = 16 - \sqrt {x + 1} \\
\Leftrightarrow 4\sqrt {x + 1} - 3\sqrt {x + 1} + 2\sqrt {x + 1} + \sqrt {x + 1} = 16\\
\Leftrightarrow 4\sqrt {x + 1} = 16\\
\Leftrightarrow \sqrt {x + 1} = 4\\
\Leftrightarrow x + 1 = {4^2}\\
\Leftrightarrow x + 1 = 16\\
\Leftrightarrow x = 15
\end{array}\)
