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Respostas
Resposta:
a) x' = 3 + √2
x" = 3 - √2
b) x' = 4
x" = -7
c) x' = 6 + 4√2
x" = 6 - 4√2
d) x' = -4
x" = -4
e) x' =
x" =
f) x' = 5
x" = 0
g) x' = 5
x" = -5
h) x' = 5√2
x" = -5√2
Explicação passo-a-passo:
a) x² - 6x + 7 = 0
Δ = (-6)² - 4 . 1 . 7
Δ = 36 - 28
Δ = 8
x' = -(-6) + √8 / 2 . 1
x' = 6 + 2√2 / 2
x' = 3 + √2
x" = -(-6) - √8 / 2 . 1
x" = 6 - 2√2 / 2
x" = 3 - √2
b) x² + 3x - 28 = 0
Δ = (3)² - 4 . 1 . -28
Δ = 9 + 112
Δ = 121
x' = -(3) + √121 / 2 . 1
x' = -3 + 11 / 2
x' = 8/2
x' = 4
x" = -(3) - √121 / 2 . 1
x" = -3 - 11 / 2
x" = -14/2
x" = -7
c) 4x² - 12x + 7 = 0
Δ = (-12)² - 4 . 4 . 7
Δ = 144 - 112
Δ = 32
x' = -(-12) + √32 / 2 . 1
x' = 12 + 4√2 / 2
x' = 6 + 4√2
x" = -(-12) - √32 / 2. 1
x" = 12 - 4√2 / 2
x" = 6 - 4√2
d) x² + 8x + 16 = 0
Δ = (8)² - 4 . 1 . 16
Δ = 64 - 64
Δ = 0
x' = -(8) + √0 / 2 . 1
x' = -8/2
x' = -4
x" -(8) - √0 / 2 . 1
x" = -8/2
x" = -4
e) 3x² - 2x + 1 = 0
Δ = (-2)² - 4 . 3 . 1
Δ = 4 - 12
Δ = 4 - 12
Δ = -8
f) x² - 5x = 0
Δ = (-5)² - 4 . 1 . 0
Δ= 25 - 0
Δ = 25
x' = -(-5) + √25 / 2 . 1
x' = 5 + 5 / 2
x' = 10/2
x' = 5
x" = -(-5) - √25 / 2 . 1
x' = 5 - 5 / 2
x' = 0/2
x' = 0
g) x² - 25 = 0
Δ = (0)² - 4 . 1 . -25
Δ = 0 + 100
Δ = 100
x' = -(0) + √100 / 2 . 1
x' =10/2
x' = 5
x" = -(0) - √100 / 2 . 1
x" = -10/2
x" = -5
h) 2x² - 100 = 0
Δ = (0)² - 4 . 2 . -100
Δ = 0 + 800
Δ = 800
x' = -(0) + √800 / 2 . 2
x' = 0 + 20√2 / 4
x' = 5√2
x" = -(0) - √800 / 2 . 2
x" = 0 - 20√2 / 4
x" = -5√2