Առաջադրանքներ՝ 632 – 635

ա) x² — 6x + 8 = 0

D = b² — 4ac
D = 36 — 32 = 4

4 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 6 + 2 / 2 = 4
X₂ = 6 — 2 / 2 = 2

բ) x² — 2x — 15 = 0

D = b² — 4ac
D = 4 + 60 = 64

64 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 2 + 8 / 2 = 5
X₂ = 2 — 8 / 2 = -3

գ) x² + 6x + 8 = 0

D = b² — 4ac
D = 36 — 32 = 4

4 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = -6 + 2 / 2 = -2
X₂ = -6 — 2 / 2 = -4

դ) x² + 2x — 15 = 0

D = b² — 4ac
D = 4 + 60 = 64

64 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = -2 + 8 / 2 = 3
X₂ = -2 — 8 / 2 = -5

ե) x² + 20x + 51 = 0

D = b² — 4ac
D = 400 — 204 = 196

196 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = -20 + 14 / 2 = -3
X₂ = -20 — 14 / 2 = -17

զ) x² — 22x — 23 = 0

D = b² — 4ac
D = 484 + 92 = 576

576 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = -22 + 24 / 2 = 1
X₂ = -22 — 24 / 2 = -23

է) x² — 20x + 69 = 0

D = b² — 4ac
D = 400 — 276 = 124

124 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 20 + √124 / 2
X₂ = 20 — √124 / 2

ը) x² + 22x + 21 = 0

D = b² — 4ac
D = 484 — 84 = 400

400 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = -22 + 20 / 2 = -1
X₂ = -22 — 20 / 2 = -21

ա) x² — 4x + 4 = 0

D = b² — 4ac
D = 16 — 16 = 0

0 = 0

X_{1, 2} = -b/2

X_{1, 2} = 4/2 = 2

բ) x² — 8x + 20 = 0

D = b² — 4ac
D = 64 — 80 = -16

-16 < 0

X_{1, 2} = -b/2 ± √D/4

X_{1, 2} = 8/2 ± (-4/2)

X₁ = 4 — 2 = 2
X₂ = 4 + 2 = 6

գ) x² — 2 1/2x + 1 = 0

D = b² — 4ac
D = 25/4 — 4 = 9/4

9/4 > 0

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 2 1/2 + 3/2 / 2 = 5/2 + 3/2 / 2 = 8/2 / 2 = 8/4
X₂ = 2 1/2 — 3/2 / 2 = 5/2 — 3/2 / 2 = 2/2 / 2 = 1/2

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