РЕШИТЕ ПЛИЗ КВАДРАТНОЕ УРАВНЕНИЕ : 4(4x−23)^2−19(4x−23)+12=0

Question

РЕШИТЕ ПЛИЗ КВАДРАТНОЕ УРАВНЕНИЕ :
4(4x−23)^2−19(4x−23)+12=0

Answer 1

Решение
4(4x−23)^2−19(4x−23)+12=0
4x - 23 = z
4z² - 19z + 12 = 0
D = 361 - 4*4*12 = 169
z₁ = (19 - 13)/8
z₁ = 0,75
z₂ = (19 + 13)/8
z₂ = 32/8
z₂ = 4

4x - 23 = 0,75
4x = 0,75 + 23
x₁ = 23,75/4
x₁ = 5,9375

4x - 23 = 4
4x = 4 + 23
4x = 27
x₂ = 6,75
 
Ответ: x₁ = 5,9375 ; x₂ = 6,75

Comments

z₁ = (19 - 11)/8
z₁ = 1
z₂ = (19 + 11)/8
z₂ = 30/8
z₂ = 3,75

4x - 23 = 1
4x = 1 + 23
x₁ = 24/4
x₁ = 6

4x - 23 = 3,75
4x = 3,75 + 23
4x = 26,75
x₂ = 6,6875

Ответ: x₁ = 6 ; x₂ = 6,6875

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D = 361 - 4*4*12 = 169
z₁ = (19 - 13)/8
z₁ = 6/8
z₂ = (19 + 13)/8
z₂ = 4

4x - 23 = 0,75
4x =23,75
x₁ = 5,9375

4x - 23 = 4
4x = 27
x₂ = 6,75

Ответ: x₁ = 5,9375 ; x₂ = 6,75