Đáp án:
$\begin{array}{l}
1.135\\
a){2^{3n}} < {3^{2n}}\\
\Rightarrow {\left( {{2^3}} \right)^n} < {\left( {{3^2}} \right)^n}\\
\Rightarrow {8^n} < {9^n}\left( {Sai} \right)\\
b)\sqrt {{x^2}} = \left| x \right| = \left[ \begin{array}{l}
x\,khi:x \ge 0\\
- x\,khi:x \le 0
\end{array} \right.\\
\Rightarrow \forall x \in R:Sai\\
c)Khi:x > 0\\
\Rightarrow {x^2} > x\\
\Rightarrow \frac{{{x^2}}}{x} > \frac{x}{x}\\
\Rightarrow x > 1\\
Khi:0 < x < 1 \Rightarrow Sai\\
1.136\\
a){x^2} > 0\\
\Rightarrow \left| x \right| > 0\\
\Rightarrow \left[ \begin{array}{l}
x > 0\\
x < 0
\end{array} \right.\\
x > 0 \Rightarrow Sai\\
b){x^2} > x\\
\Rightarrow {x^2} - x > 0\\
\Rightarrow x.\left( {x - 1} \right) > 0\\
\Rightarrow \left[ \begin{array}{l}
x > 1\\
x < 0
\end{array} \right.\\
x < 0 \Rightarrow sai\\
c)x < 1\\
\Rightarrow \left[ \begin{array}{l}
x.x < 1.x\,khi:x > 0\\
x.x > 1.x\,khi:x < 0
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{x^2} < x\,khi:x > 0\\
{x^2} > x\,khi:x < 0
\end{array} \right.\\
1.137\\
a)x < y\\
\Rightarrow x.x < y.y\left( {do:x;y > 0} \right)\\
\Rightarrow {x^2} < {y^2}\\
b){x^2} < {y^2}\\
\Rightarrow \sqrt {{x^2}} < \sqrt {{y^2}} \\
\Rightarrow \left| x \right| < \left| y \right|\\
\Rightarrow x < y\left( {do:x;y > 0 \Rightarrow \left\{ \begin{array}{l}
\left| x \right| = x\\
\left| y \right| = y
\end{array} \right.} \right)\\
1.138\\
a)a < b\\
\Rightarrow \sqrt a < \sqrt b \left( {do:a,b > 0} \right)\\
b)\sqrt a < \sqrt b \\
\Rightarrow \sqrt a .\sqrt a < \sqrt b .\sqrt b \\
\Rightarrow a < b
\end{array}$
