Đáp án:
\(\begin{array}{l}
1,\\
a,\,\,\,4\sqrt 2 \\
b,\,\,\,\,2\sqrt 2 \\
c,\,\,\,\, - 15\sqrt 2 \\
d,\,\,\,\, - \sqrt 2 \\
2,\\
a,\\
x = 17\\
b,\\
x = \dfrac{{25}}{4}\\
c,\\
x = - 1\\
d,\\
x = 24\\
e,\\
x = 9
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
2\sqrt 2 - 3\sqrt {18} + 4\sqrt {32} - \sqrt {50} \\
= 2\sqrt 2 - 3\sqrt {9.2} + 4\sqrt {16.2} - \sqrt {25.2} \\
= 2\sqrt 2 - 3.\sqrt {{3^2}.2} + 4\sqrt {{4^2}.2} - \sqrt {{5^2}.2} \\
= 2\sqrt 2 - 3.3\sqrt 2 + 4.4\sqrt 2 - 5\sqrt 2 \\
= 2\sqrt 2 - 9\sqrt 2 + 16\sqrt 2 - 5\sqrt 2 \\
= 4\sqrt 2 \\
b,\\
\sqrt 8 - 3\sqrt 2 + \sqrt {50} - 2\sqrt 2 \\
= \sqrt {4.2} + \sqrt {25.2} + \left( { - 3\sqrt 2 - 2\sqrt 2 } \right)\\
= \sqrt {{2^2}.2} + \sqrt {{5^2}.2} - 5\sqrt 2 \\
= 2\sqrt 2 + 5\sqrt 2 - 5\sqrt 2 \\
= 2\sqrt 2 \\
c,\\
\sqrt {50} - 3\sqrt {98} + 2\sqrt 8 + 3\sqrt {32} - 5\sqrt {18} \\
= \sqrt {25.2} - 3\sqrt {49.2} + 2\sqrt {4.2} + 3\sqrt {16.2} - 5\sqrt {9.2} \\
= \sqrt {{5^2}.2} - 3\sqrt {{7^2}.2} + 2.\sqrt {{2^2}.2} + 3\sqrt {{4^2}.2} - 5\sqrt {{3^2}.2} \\
= 5\sqrt 2 - 3.7\sqrt 2 + 2.2\sqrt 2 + 3.4\sqrt 2 - 5.3\sqrt 2 \\
= 5\sqrt 2 - 21\sqrt 2 + 4\sqrt 2 + 12\sqrt 2 - 15\sqrt 2 \\
= - 15\sqrt 2 \\
d,\\
\sqrt {18} - 2\sqrt {50} + 3\sqrt 8 \\
= \sqrt {9.2} - 2\sqrt {25.2} + 3\sqrt {4.2} \\
= \sqrt {{3^2}.2} - 2\sqrt {{5^2}.2} + 3\sqrt {{2^2}.2} \\
= 3\sqrt 2 - 2.5\sqrt 2 + 3.2\sqrt 2 \\
= 3\sqrt 2 - 10\sqrt 2 + 6\sqrt 2 \\
= - \sqrt 2 \\
2,\\
a,\\
DKXD:\,\,\,x \ge 1\\
2\sqrt {36x - 36} - \dfrac{1}{3}\sqrt {9x - 9} - 4\sqrt {4x - 4} + \sqrt {x - 1} = 16\\
\Leftrightarrow 2.\sqrt {36\left( {x - 1} \right)} - \dfrac{1}{3}.\sqrt {9\left( {x - 1} \right)} - 4\sqrt {4\left( {x - 1} \right)} + \sqrt {x - 1} = 16\\
\Leftrightarrow 2.\sqrt {{6^2}\left( {x - 1} \right)} - \dfrac{1}{3}.\sqrt {{3^2}\left( {x - 1} \right)} - 4\sqrt {{2^2}\left( {x - 1} \right)} + \sqrt {x - 1} = 16\\
\Leftrightarrow 2.6\sqrt {x - 1} - \dfrac{1}{3}.3\sqrt {x - 1} - 4.2\sqrt {x - 1} + \sqrt {x - 1} = 16\\
\Leftrightarrow 12\sqrt {x - 1} - \sqrt {x - 1} - 8\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 = 17\\
b,\\
DKXD:\,\,\,x \ge 0\\
4\sqrt x - 2\sqrt {9x} + \sqrt {16x} = 5\\
\Leftrightarrow 4\sqrt x - 2.\sqrt {{3^2}.x} + \sqrt {{4^2}.x} = 5\\
\Leftrightarrow 4\sqrt x - 2.3\sqrt x + 4\sqrt x = 5\\
\Leftrightarrow 4\sqrt x - 6\sqrt x + 4\sqrt x = 5\\
\Leftrightarrow 2\sqrt x = 5\\
\Leftrightarrow \sqrt x = \dfrac{5}{2}\\
\Leftrightarrow x = {\left( {\dfrac{5}{2}} \right)^2}\\
\Leftrightarrow x = \dfrac{{25}}{4}\\
c,\\
DKXD:\,\,\,x \ge - 5\\
\sqrt {4x + 20} - 3\sqrt {5 + x} + \dfrac{4}{3}\sqrt {9x + 45} = 6\\
\Leftrightarrow \sqrt {4.\left( {x + 5} \right)} - 3\sqrt {x + 5} + \dfrac{4}{3}.\sqrt {9\left( {x + 5} \right)} = 6\\
\Leftrightarrow \sqrt {{2^2}\left( {x + 5} \right)} - 3\sqrt {x + 5} + \dfrac{4}{3}\sqrt {{3^2}.\left( {x + 5} \right)} = 6\\
\Leftrightarrow 2\sqrt {x + 5} - 3\sqrt {x + 5} + \dfrac{4}{3}.3\sqrt {x + 5} = 6\\
\Leftrightarrow 2\sqrt {x + 5} - 3\sqrt {x + 5} + 4\sqrt {x + 5} = 6\\
\Leftrightarrow 3\sqrt {x + 5} = 6\\
\Leftrightarrow \sqrt {x + 5} = 2\\
\Leftrightarrow x + 5 = {2^2}\\
\Leftrightarrow x + 5 = 4\\
\Leftrightarrow x = - 1\\
d,\\
DKXD:\,\,\,x \ge - 1\\
12\sqrt {\dfrac{{x + 1}}{{16}}} + \dfrac{1}{2}\sqrt {4x + 4} - \dfrac{2}{3}\sqrt {9x + 9} - 10 = 0\\
\Leftrightarrow 12.\sqrt {\dfrac{1}{{16}}\left( {x + 1} \right)} + \dfrac{1}{2}\sqrt {4.\left( {x + 1} \right)} - \dfrac{2}{3}\sqrt {9\left( {x + 1} \right)} - 10 = 0\\
\Leftrightarrow 12.\sqrt {{{\left( {\dfrac{1}{4}} \right)}^2}.\left( {x + 1} \right)} + \dfrac{1}{2}\sqrt {{2^2}.\left( {x + 1} \right)} - \dfrac{2}{3}\sqrt {{3^2}.\left( {x + 1} \right)} - 10 = 0\\
\Leftrightarrow 12.\dfrac{1}{4}\sqrt {x + 1} + \dfrac{1}{2}.2\sqrt {x + 1} - \dfrac{2}{3}.3\sqrt {x + 1} - 10 = 0\\
\Leftrightarrow 3\sqrt {x + 1} + \sqrt {x + 1} - 2\sqrt {x + 1} - 10 = 0\\
\Leftrightarrow 2\sqrt {x + 1} - 10 = 0\\
\Leftrightarrow \sqrt {x + 1} = 5\\
\Leftrightarrow x + 1 = {5^2}\\
\Leftrightarrow x + 1 = 25\\
\Leftrightarrow x = 24\\
e,\\
DKXD:\,\,\,x \ge 0\\
\sqrt {9x} - 5\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow \sqrt {{3^2}.x} - 5\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow 3\sqrt x - 5\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow - 2\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow - 2\sqrt x + 4\sqrt x = 6\\
\Leftrightarrow 2\sqrt x = 6\\
\Leftrightarrow \sqrt x = 3\\
\Leftrightarrow x = {3^2}\\
\Leftrightarrow x = 9
\end{array}\)
