Question

Bài 2: Giải pt, bpt sau:

4) \(8^x \leq 4.(4-2^x)\)

5) \(\left(\dfrac{1}{3}\right)^{\frac{2}{x}} + 3.\left(\dfrac{1}{3}\right)^{\frac{1}{x}+1} > 12\)

Answer 1

a.

Đặt \(2^x=t>0\)

\(\Rightarrow t^3\le4\left(4-t\right)\Rightarrow t^3+4t-16\le0\)

\(\Rightarrow\left(t-2\right)\left(t^2+2t+8\right)\le0\)

\(\Rightarrow t\le2\)

\(\Rightarrow2^x\le2\Rightarrow x\le1\)

b.

Đặt \(\left(\dfrac{1}{3}\right)^{\dfrac{1}{x}}=t>0\)

\(\Rightarrow t^2+3.\dfrac{1}{3}t>12\)

\(\Leftrightarrow t^2+t-12>0\)

\(\Leftrightarrow\left(t+4\right)\left(t-3\right)>0\)

\(\Leftrightarrow t>3\)

\(\Rightarrow\left(\dfrac{1}{3}\right)^{\dfrac{1}{x}}>3\)

\(\Rightarrow\dfrac{1}{x}< -1\)

\(\Rightarrow\dfrac{x+1}{x}< 0\)

\(\Rightarrow-1< x< 0\)