Question

Решите неравенства:

$1) 0,5^{x2-x} textgreater frac{1}{4} 2) 5^{2x} textless frac{1}{25}$

Answer 1

$1) 0.5^{ x^{2} -x} textgreater frac{1}{4}$
$frac{1}{2}^{x^{2}-x} textgreater frac{1}{2}^{2}$
$x^{2} - x textless 2$
x² - x - 2 < 0
x1 = 1; x2 = -2
x ∈ ( -1; 2 )

$2) 5^{2x} textless 5^{-2}$
2x < -2
2x+ 2 < 0
2(x+1) < 0
x∈(-∞; -1)