Question

inequação exponencial

Answer 1

$(2^{-x})^{3x+1}*(2^2)^{1+2x-x^2} \geq (2^{-3})^{x-1} \\ 2^{-3x^2-x}*2^{-2x^2+4x+2} \geq 2^{-3x+3} \\ 2^{-5x^2+3x+2} \geq 2^{-3x+3} \\ -5x^2+3x+2 \geq -3x+3 \\ -5x^2+6x-1 \geq 0$

Δ=36-20
Δ=16

$x_1= \frac{-6+4}{-10} \\ x_1= \frac{-2}{-10} \\ x_1= \frac{1}{5} \\ x_2= \frac{-6-4}{-10} \\ x_2= \frac{-10}{-10} \\ x_2= 1$

$S=[ \frac{1}{5} ;1]$