Question

Решить неравенство (x+3)/(x-2)>0 и найти область значений

Answer 1

(x+3)/(x-2)>0 |*(x-2)
(x+3)*(x-2)>0*(x-2)
x²-2x+3x-6>0
x²+x-6>0
a=1 b=1 c=-6
x₁=(-b-√(b²-4ac))/2a=
=(-1-√(1+24))/(2*1)=
=(-1-√25)/2=
=(-1-5)/2=
=-6/2=
=-3

x₂=(-b+√(b²-4ac))/2a=
=(-1+√(1+24))/(2*1)=
=(-1+√25)/2=
=(-1+5)/2=
=4/2=
=2