110-ա,գ. Լուծեք անհավասարումը․

ա) x² – 3 > 0

x² – 3 = 0
(x – √3)(x + √3) = 0

⌈x – √3 = 0
⌊x + √3 = 0

⌈x = √3
⌊x = -√3 

x² – 3 > 0

x ∈ (-∞; -√3) ∪ (√3; +∞)

գ) 2 – x² < 0

2 – x² = 0
(√2 – x)(√2 + x) = 0

⌈√2 – x = 0
⌊√2 + x = 0

⌈-x = √2
⌊x = √2

[x = -√2

2 – x² < 0

x ∈ (-√2; √2)

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ՏՆԱՅԻՆ․

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110-բ,դ. Լուծեք անհավասարումը․

բ) x² – 5 < 0

x² – 5 = 0
(x – √5)(x + √5) = 0

⌈x – √5 = 0
⌊x + √5 = 0

⌈x = √5
⌊x = -√5 

x² – 5 < 0

x ∈ (-√5; √5)

դ) 13 – x² > 0

13 – x² = 0
(√13 – x)(√13 + x) = 0

⌈√13 – x = 0
⌊√13 + x = 0

⌈-x = √13
⌊x = √13

⌈x = -√13
⌊x = √13

13 – x² > 0

x ∈ (-∞; -√13) ∪ (√13; +∞)

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111-բ,դ. Լուծեք անհավասարումը․

բ) 1,3x² – 2x < 0

1,3x² – 2x = 0
x(1,3x – 2) = 0

⌈x = 0
⌊1,3x – 2 = 0

⌈x = 0
⌊1,3x = 2

⌈x = 0
⌊x = ²⁰/₁₃

1,3x² – 2x < 0

x ∈ (0; ²⁰/₁₃)

դ) ⁷/₈x² – 1 ³/₅ > 0

⁷/₈x² – ⁸/₅ = 0
(√⁷/₈x – √⁸/₅)(√⁷/₈x + √⁸/₅) = 0

⌈√⁷/₈x – √⁸/₅ = 0
⌊√⁷/₈x + √⁸/₅ = 0

⌈√⁷/₈x = √⁸/₅
⌊√⁷/₈x = -√⁸/₅

⌈x = ^√8/₅ : ⁷/_√8 = ^√8/₅ * ^√8/₇ = ⁸/₃₅
⌊x = –^√8/₅ : ⁷/_√8 = –^√8/₅ * ^√8/₇ = –⁸/₃₅

⁷/₈x² – 1 ³/₅ > 0

x ∈ (-∞; –⁸/₃₅) ∪ (⁸/₃₅; +∞)

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113-բ,դ,զ. Լուծեք անհավասարումը․

բ) x² + 4x + 3 < 0

x² + 4x + 3 = 0
a = 1
b = 4
c = 3

D = b² – 4ac = 16 – 4 * 1 * 3 = 16 – 12 = 4

x = ^{-b + √D}/_2a = ^{-4 + √4}/_{2 * 1} = ^{-4 + 2}/₂
x₁ = ^{-4 + 2}/₂ = ^-2/₂ = -1
x₂ = ^{-4 – 2}/₂ = ^-6/₂ = -3

x² + 4x + 3 < 0

x ∈ (-3; -1)

դ) x² – 5x + 4 > 0

x² – 5x + 4 = 0
a = 1
b = -5
c = 4

D = b² – 4ac = 25 – 4 * 1 * 4 = 25 – 16 = 9

x = ^{-b + √D}/_2a = ^{5 + √9}/_{2 * 1} = ^{5 + 3}/₂
x₁ = ^{5 + 3}/₂ = ⁸/₂ = 4
x₂ = ^{5 – 3}/₂ = ²/₂ = 1

x² – 5x + 4 > 0

x ∈ (-∞; 1) ∪ (4; +∞)

զ) 4x² – x – 3 < 0

4x² – x – 3 = 0
a = 4
b = -1
c = -3

D = b² – 4ac = 1 – 4 * 4 * -3 = 1 + 48 = 49

x = ^{-b + √D}/_2a = ^{1 + √49}/_{2 * 4} = ^{1 + 7}/₈
x₁ = ^{1 + 7}/₈ = ⁸/₈ = 1
x₂ = ^{1 – 7}/₈ = ^-6/₈ = –³/₄

4x² – x – 3 < 0

x ∈ (-³/₄; 1)

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114-բ,դ,զ. Լուծեք անհավասարումը․

բ) 0,5x² + 88x + 24 < 0

0,5x² + 88x + 24 = 0
a = 0,5
b = 88
c = 24

D = b² – 4ac = 7744 – 4 * 24 * 0,5 = 7696

x = ^{-b + √D}/_2a = ^{-88 + √7696}/_{2 * 0,5} = -88 + 16√481
x₁ = -88 + 4√481 ≈ -0,27315
x₂ = -88 – 4√481 ≈ -175,72685

0,5x² + 88x + 24 < 0

x ∈ (-175,72685; -0,27315)

դ) 4x + ¹/₄x² + 12 > 0

¹/₄x² + 4x + 12 = 0
a = 0,25
b = 4
c = 12

D = b² – 4ac = 16 – 4 * 0,25 * 12 = 16 – 12 = 4

x = ^{-b + √D}/_2a = ^{-4 + √4}/_{2 * 0,25} = ^{-4 + 2}/_0,5
x₁ = ^{-4 + 2}/_0,5 = ^-2/_0,5 = -4
x₂ = ^{-4 – 2}/_0,5 = ^-6/_0,5 = -12

¹/₄x² + 4x + 12 > 0

x ∈ (-∞; -12) ∪ (-4; +∞)

զ) 8x² – 3 – 2x > 0

8x² – 2x – 3 = 0
a = 8
b = -2
c = -3

D = b² – 4ac = 4 – 4 * 8 * -3 = 4 + 96 = 100

x = ^{-b + √D}/_2a = ^{2 + √100}/_{2 * 8} = ^{2 + 10}/₁₆
x₁ = ^{2 + 10}/₁₆ = ¹²/₁₆ = ³/₄
x₂ = ^{2 – 10}/₁₆ = ^-8/₁₆ = –¹/₂

8x² – 3 – 2x > 0

x ∈ (-∞; –¹/₂) ∪ (³/₄; +∞)