Đáp án:
\(\begin{array}{l}
a)x = 100\\
b)0 \le x < 25\\
c)\left[ \begin{array}{l}
x = 4\\
x = - 4
\end{array} \right.\\
d)\left[ \begin{array}{l}
x = \sqrt 7 \\
x = - \sqrt 7
\end{array} \right.\\
e)x = 5\\
f)x = 2
\end{array}\)
\(\begin{array}{l}
g)x = \dfrac{5}{3}\\
d)A = \dfrac{{2a + 3}}{{ - b}}\\
M = 3x - 3\\
E = x - 3\\
F = 3x - 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\sqrt x = 10\\
\to x = 100\\
b)\sqrt x < 5\\
\to x < 25\\
\to 0 \le x < 25\\
c)2\left| x \right| = 8\\
\to \left| x \right| = 4\\
\to \left[ \begin{array}{l}
x = 4\\
x = - 4
\end{array} \right.\\
d){x^2} = 7\\
\to \left[ \begin{array}{l}
x = \sqrt 7 \\
x = - \sqrt 7
\end{array} \right.\\
e)DK:x \ge \dfrac{1}{2}\\
\sqrt {2x - 1} = 3\\
\to 2x - 1 = 9\\
\to x = 5\\
f)DK:x \ge 1\\
2\sqrt {x - 1} + 3\sqrt {x - 1} = 5\\
\to 5\sqrt {x - 1} = 5\\
\to \sqrt {x - 1} = 1\\
\to x - 1 = 1\\
\to x = 2
\end{array}\)
\(\begin{array}{l}
g)DK:4 \ge x \ge \dfrac{1}{2}\\
\sqrt {2x - 1} = \sqrt {4 - x} \\
\to 2x - 1 = 4 - x\\
\to 3x = 5\\
\to x = \dfrac{5}{3}\\
d)A = \sqrt {\dfrac{{{{\left( {3 + 2a} \right)}^2}}}{{{b^2}}}} \\
= \left| {\dfrac{{3 + 2a}}{b}} \right|\\
= \dfrac{{2a + 3}}{{ - b}}\\
M = \left| {x - 2} \right| + 2x - 1\\
= x - 2 + 2x - 1\\
= 3x - 3\\
E = \left| {3 - x} \right| = - \left( {3 - x} \right)\\
= x - 3\\
F = \sqrt {{{\left( {x - 3} \right)}^2}} + 2x\\
= \left| {x - 3} \right| + 2x\\
= x - 3 + 2x = 3x - 3
\end{array}\)
