Question

Решите неравенство 1) 3x^2+3x-6<(x-1)^2 2) 3x^2-5x-32<(x-7)^2 3) 2x^2+7x-13>(x-5)^2 4) 2x^2+14x-20>(x-6)^2 5) 3x^2+10x+19>(x+7)^2

Answer 1

1
3x²+3x-6-x²+2x-1<0
2x²+5x-7<0
D=25+56=81
x1=(-5-9)/4=-3,5 U x2=(-5+9)/4=1
x∈(-3,5;1)
2
3x²-5x-32-x²+14x-49<0
2x²+9x-81<0
D=81+648=729
x1=(-9-27)/4=-9 U x2=(-9+27)/4=4,5
x∈(-9;4,5)
3
2x²+7x-13-x²+10x-25>0
x²+17x-38>0
x1+x2=-17 U x1*x2=-38
x1=-19 U x2=2
x∈(-∞;-19) U (2;∞)
4
2x²+14x-20-x²+12x-36>0
x²+26x-56>0
x1+x2=-26 U x1*x2=-56
x1=-28 U x2=2
x∈(-∞;-28) U (2;∞)
5
3x²+10x+19-x²-14x-49>0
2x²-4x-30>0
x²-2x-15>0
x1+x2=2 U x1*x2=-15
x1=-3 U x2=5
x∈(-∞;-3) U (5;∞)