Advertisements (Quảng cáo)
Tìm x, biết:
a) \(\sqrt {25x} = 35\);
b) \(\sqrt {4x} \le 162\);
c) \(3\sqrt x = \sqrt {12} \);
d) \(2\sqrt x \ge 10\).
Gợi ý làm bài
\(\eqalign{
& a)\,\sqrt {25x} = 35 \Leftrightarrow 5\sqrt x = 35 \cr
& \Leftrightarrow \sqrt x = 7 \Leftrightarrow x = 49 \cr} \)
Advertisements (Quảng cáo)
\(\eqalign{
& b)\,\sqrt {4x} \le 162 \Leftrightarrow 2\sqrt x \le 162 \cr
& \Leftrightarrow \sqrt x \le 81 \Leftrightarrow x \le 6561 \cr} \)
Suy ra : \(0 \le x \le 6561\)
\(\eqalign{
& b)\,3\sqrt x = 12 \Leftrightarrow 3\sqrt x = 2\sqrt 3 \cr
& \Leftrightarrow \sqrt x = {2 \over 3}\sqrt 3 \Leftrightarrow x = {\left( {{2 \over 3}\sqrt 3 } \right)^2} \cr
& \Leftrightarrow x = – {4 \over 3} \cr} \)
d) \(2\sqrt x \ge \sqrt {10} \Leftrightarrow \sqrt x \ge {{\sqrt {10} } \over 2} \Leftrightarrow x = {5 \over 2}\)