Question

B) 3x² + 22x – 16 = 0;
Полное решение)


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Answer 1

Общий вид квадратного уравнения:

ax² + bx + c = 0

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Способ 1 (через D₁).

3x² + 22x - 16 = 0

a = 3, b = 22, c = - 16,

k = b/2 =

= 22/2 = 11

D₁ = k² - ac = 11² - 3 · ( -16 )

= 121 + 48 = 169 = 13²

x₁,₂ = ( -k ± √D₁)/a = ( -11 ± √13² )/3 =

= ( -11 ± 13 )/3

x₁ = ( -11 - 13 )/3 = - 24/3 = -8

x₂ = ( -11 + 13 )/3 = 2/3

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Способ 2 (через D).

3x² + 22x - 16 = 0

a = 3, b = 22 , c = - 16

D = b² - 4ac = 22² - 4 · 3 · ( -16 ) =

= 484 + 192 = 676 = 26²

x₁,₂ = ( -b ± √D )/2a = ( -22 ± √26² )/2 · 3 =

= ( -22 ± 26 )/6

x₁ = ( -22 - 26 )/6 = - 48/6 = -8

x₂ = ( -22 + 26)/6 = 4/6 = 2/3

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Ответ: -8; 2/3.