1.
x²-4x+3 < 0
Δ=(-4)²-4·1·3=16-12=4, √Δ=√4=2
x1=(4-2)/2
x1=1
x2=(4+2))/2
x2=3
x∈(1,3)
2.
-2x²+4x-5 < 0 |:(-1)
2x²-4x+5 > 0
Δ=(-4)²-4·2·5=16-40=-24 , Δ < 0
x∈R
3.
4x²-9 > 0
(2x+3)(2x-3) > 0
2x+3=0 ∨ 2x-3=0
2x=-3|:2 ∨ 2x=3|:2
x=-3/2 ∨ x=3/2
x∈(-∞,-3/2)∪(3/2,∞)
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1.
x²-4x+3 < 0
Δ=(-4)²-4·1·3=16-12=4, √Δ=√4=2
x1=(4-2)/2
x1=1
x2=(4+2))/2
x2=3
x∈(1,3)
2.
-2x²+4x-5 < 0 |:(-1)
2x²-4x+5 > 0
Δ=(-4)²-4·2·5=16-40=-24 , Δ < 0
x∈R
3.
4x²-9 > 0
(2x+3)(2x-3) > 0
2x+3=0 ∨ 2x-3=0
2x=-3|:2 ∨ 2x=3|:2
x=-3/2 ∨ x=3/2
x∈(-∞,-3/2)∪(3/2,∞)