a) x2−4x<4
x2−4x<4∧x2−4x>−4
x2−4x−4<0∧x2−4x+4>0
x2−4x+4−4−4<0∧(x−2)2>0
(x−2)2<8∧x−2=0
∣x−2∣<22∧x∈R−{2}
(x−2<22∧x−2>−22)∧x∈R−{2}
(x<2+22∧x>2−22)∧x∈R−{2}
x∈(2−22, 2+22)∧x∈R−{2}
x∈(2−22, 2)∪(2, 2+22)
Odp. x∈(2−22, 2)∪(2, 2+22).
b) x2−6x<9
x2−6x<9∧x2−6x>−9
x2−6x−9<0∧x2−6x+9>0
x2−6x+9−9−9<0∧(x−3)2>0
(x−3)2<18∧x−3=0
∣x−3∣<32∧x∈R−{3}
(x−3<32∧x−3>−32)∧x∈R−{3}
(x<3+32∧x>3−32)∧x∈R−{3}
x∈(3−32, 3+32)∧x∈R−{3}
x∈(3−32, 3)∪(3, 3+32)
Odp. x∈(3−32, 3)∪(3, 3+32).
c) x2+3x+1≤1
x2+3x+1≤1 ∧ x2+3x+1≥−1
x2+3x≤0 ∧ x2+3x+2≥0
x(x+3)≤0 ∧ (x+2)(x+1)≥0
x∈⟨−3, 0⟩ ∧ x∈(−∞,−2⟩∪⟨−1,+∞)
x∈⟨−3,−2⟩∪⟨−1, 0⟩
Odp. x∈⟨−3,−2⟩∪⟨−1, 0⟩.
d) x2+6x−1≤6
x2+6x−1≤6∧x2+6x−1≥−6
x2+6x−7≤0∧x2+6x+5≥0
(x+7)(x−1)≤0∧(x+5)(x+1)≥0
x∈⟨−7, 1⟩∧x∈(−∞,−5⟩∪⟨−1,+∞)
x∈⟨−7,−5⟩∪⟨−1, 1⟩
Odp. x∈⟨−7,−5⟩∪⟨−1, 1⟩.
