Question

Решите нерпвенство:
2x^2-12x-59<-3x^2-5x-25

Answer 1

Відповідь:

x∈ $(-2, \frac{17}{5} )$

Пояснення:

$2x^2-12x-59 < -3x^2-5x-25\\\\2x^2-12x-59+3x^2+5x+25 < 0\\\\5x^2-7x-34 < 0\\\\5x^2+10x-17x-34 < 0\\\\5(x+2)-17x(x+2) < 0\\\\(x+2)(5x-17) < 0\\\\\left \{ {{x+2 < 0} \atop {5x-17 > 0} \right. \\\left \{ {{x+2 > 0} \atop {5x-17 < 0}} \right. \\\\\left \{ {{x < -2} \atop {x > \frac{17}{5 }} \right. \\ \left \{ {{x > -2} \atop {x < \frac{17}{5} }} \right.$

x∈ $(-2, \frac{17}{5} )$