Nội dung bài giảng
Tìm x, biết:
a) \(\sqrt {{{\left( {2{\rm{x}} - 1} \right)}^2}} = 3\)
b) \({5 \over 3}\sqrt {15{\rm{x}}} - \sqrt {15{\rm{x}}} - 2 = {1 \over 3}\sqrt {15{\rm{x}}} \)
Hướng dẫn làm bài:
a)
\(\eqalign{
& \sqrt {{{\left( {2{\rm{x}} - 1} \right)}^2}} = 3 \cr
& \Leftrightarrow \left| {2{\rm{x}} - 1} \right| = 3 \cr
& \Leftrightarrow \left\{ \matrix{
3 \ge 0 \hfill \cr
\left[ \matrix{
2{\rm{x}} - 1 = 3 \hfill \cr
2{\rm{x}} - 1 = - 3 \hfill \cr} \right. \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
2{\rm{x}} = 4 \hfill \cr
2{\rm{x}} = - 2 \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
x = 2 \hfill \cr
x = - 1 \hfill \cr} \right. \cr} \)
b)
\(\eqalign{
& {5 \over 3}\sqrt {15{\rm{x}}} - \sqrt {15{\rm{x}}} - 2 = {1 \over 3}\sqrt {15{\rm{x}}} \cr
& \Leftrightarrow {5 \over 3}\sqrt {15{\rm{x}}} - \sqrt {15{\rm{x}}} - {1 \over 3}\sqrt {15{\rm{x}}} = 2 \cr
& \Leftrightarrow \left( {{5 \over 3} - 1 - {1 \over 3}} \right)\sqrt {15} x = 2 \cr
& \Leftrightarrow {1 \over 3}\sqrt {15{\rm{x}}} = 2 \cr
& \Leftrightarrow \sqrt {15{\rm{x}}} = 6 \cr
& \Leftrightarrow 15{\rm{x}} = {6^2} \cr
& \Leftrightarrow x = {{12} \over 5} \cr} \)