Question

resolva as seguintes inequações​

Answer 1

Resposta:

a)

Vamos separar:

${2}^{x - 3} \geqslant \frac{1}{4}$

${2}^{x - 3} \leqslant \frac{1}{2}$

Primeira:

$x - 3 \geqslant 2$

$x \geqslant 1$

Segunda:

$x - 3 \leqslant - 1$

$x \leqslant 2$

$x ∈ [ 1, \: 2]$

b)

${e}^{x} > {e}^{ - x + 5}$

$2x > 5$

$x > \frac{5}{2}$

c)

${2}^{2x} - \frac{9}{4} {2}^{x} + \frac{1}{2} = 0$

${2}^{x} = \frac{1}{4} U {2}^{x} = 2$

$x = - 2Ux = 1$

$- 2 < x < 1$

d)

${3}^{2x} - 12 \times {3}^{x} + 27 = 0$

${3}^{x} = 3U {3}^{x} = 9$

$x = 1Ux = 2$

$x < 1Ux > 2$

e)

${e}^{2x} - (e + 1) {e}^{x} + e = 0$

${e}^{x} = 1U {e}^{x} = e$

$x = 0 \: Ux = 1$

$0 < x < 1$