Question

Tìm nghiệm của bpt \(5.9^{x^{ }}+2.15^x-3.25^x\ge0\)

A. \((-\infty;-1]\cup[1;+\infty)\)

B. \([1;+\infty)\)

C. \((-\infty;1]\)

D. \([0;1]\)

Answer 1

\(\Leftrightarrow5\left(\frac{9^x}{25^x}\right)+2\left(\frac{15^x}{25^x}\right)-3\ge0\)

\(\Leftrightarrow5\left(\frac{3}{5}\right)^x+2\left(\frac{3}{5}\right)^x-3\ge0\)

\(\Leftrightarrow\left[5\left(\frac{3}{5}\right)^x-3\right]\left[\left(\frac{3}{5}\right)^x+1\right]\ge0\)

\(\Leftrightarrow5\left(\frac{3}{5}\right)^x-3\ge0\)

\(\Leftrightarrow\left(\frac{3}{5}\right)^x\ge\frac{3}{5}\)

\(\Rightarrow x\ge1\)

Đáp án B