Question

resolver estas dos inecuaciones de segundo grado


5x – 6 ≤ -x²


x² - 12 > x

Answer 1

Respuesta:

5x – 6 ≤ -x²

$=5x - 6 + x^{2} \leq 0\\=x^{2} + 5x - 6 \leq 0\\=x^{2} +6x-x-6\leq 0\\=x(x+6)- (x+6)\leq 0\\=(x+6)(x-1)\leq 0\\\left \{ {{x+6\leq 0} \atop {x-1\geq0 }} \right. \\\left \{ {{x-1\geq0 } \atop {x+6\leq 1}} \right. \\\left \{ {{x\leq-6 } \atop {x\leq 1}} \right.$

x² - 12 > x

$= x^{2} -12-x>0\\x^{2} -x-12>0\\x^{2} +3x-4x-12>0\\x(x +3)-4(x +3)>0\\(x +3) * (x-4)>0\\\left \{ {{x +3>0} \atop {x-4>0}} \right. \\\left \{ {{ x+3<0} \atop {x-4<0}} \right.\\\left \{ {{x>-3} \atop {x>4}} \right. \\\left \{ {{x<-3} \atop {x<4}} \right.$