Найдите все возможные параметры а и b

x^2 - 8*x + a = b*|x - 6|

x^2 - 8*x + a = b*(x - 6) при x >= 6
x^2 - (8 + b)*x + a + 6*b = 0
{ x1 + x2 = 8 + b
{ x1*x2 = a + 6*b

x^2 - 8*x + a = -b*(x - 6) при x < 6
x^2 - (8 - b)*x + a - 6*b = 0
{ x3 + x4 = 8 - b
{ x3*x4 = a - 6*b

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x1 = x2 + x3 + x4

x1 + x2 - (x3 + x4) = 8 + b - (8 - b)
(x1 + x2 - (x3 + x4)) / 2 = b
(x2 + x3 + x4 + x2 - x3 - x4) / 2 = b
x2 = b

x1*x2 = a + 6*b
(b + x3 + x4)*b = a + 6*b
(b + 8 - b)*b = a + 6*b
2*b = a

x^2 - 8*x + 2*b = b*|x - 6|

x^2 - (8 + b)*x + 8*b = 0 при x >= 6
D = (8 + b)^2 - 32*b = (b - 8)^2
x1 = (8 + b + |b - 8|) / 2 >= 6 => b in R
x2 = (8 + b - |b - 8|) / 2 >= 6 => b >= 6
причём x1 = x2, когда b = 8

x^2 - (8 - b)*x - 4*b=0 при x < 6
D = (8 - b)^2 + 16*b = b^2 + 64
x1 = (8 - b + sqrt(b^2+64)) / 2 < 6 => b > 6
x2 = (8 - b - sqrt(b^2+64)) / 2 < 6 => b in R

a = 2*b при b != 8 и b > 6

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x3 = x1 + x2 + x4

(x1 + x2 - (x3 + x4)) / 2 = b
(x1 + x2 - (x1 + x2 + x4 + x4)) / 2 = b
x4 = -b

x3*x4 = a - 6*b
(x1 + x2 - b)*b = 6*b - a
(8 + b - b)*b = 6*b - a
2*b = -a

x^2 - 8*x - 2*b = b*|x - 6|

x^2 - 8*x - 2*b - b*(x - 6) = 0 при x >= 6
x^2 - (8 + b)*x + 4*b=0
D = (8 + b)^2 - 4*4*b = b^2 + 64
x1 = (8 + b + sqrt(b^2 + 64)) / 2 >= 6 => b >= -6
x2 = (8 + b - sqrt(b^2 + 64)) / 2 >= 6 => b not in R
уже понятно, что действительных корней будет меньше 4

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ответ: a = 2*b, при b != 8 и b > 6