Question

a) 2 +

b) -3 (x-2)(x+1) 0

c)

Answer 1

a)

2+(x-3)²≤x²-(5x-15)/2

2+x²+9-6x≤x²-2,5x+7,5

-6x+11≤-2,5x+7,5

3,5x≥3,5

x≥1

x∈<1;+∞)

b)

-3(x²+x-2x-2)≤0

-3x²+3x+6≤0

-3x²+3x+6=0

a=-3

b=3

c=6

Δ=b²-4ac

Δ=3²-4·(-3)·6=9+72=81

√Δ=9

x₁=9-3/-6=-1

x₂=-9-3/-6=2

x∈(-∞;-1> u <2;+∞)

c)

x²-x-6>0

x²-x-6=0

a=1

b=-1

c=-6

Δ=b²-4ac

Δ=(-1)²-4·1·(-6)=1+24=25

√Δ=5

x₁=5-(-1)/2=3

x₂=-5-(-1)/2=-2

x∈(-∞;-2) u (3;+∞)