Х^2-4x = 3√(x^2-4x+20) -10
x^2 -4x +20 ≥0 ;
Замена переменной: x^2 -4x=t
t= 3√(t+20) -10
(t +10)^2 = (3√(t+20))^2
t^2 + 20t +100 = 9(t+20)
t^2 +20t +100 -9t -180 =0
t^2 +11t -80=0
D= 11^2 -4*1*(-80) = 121 + 320 = 441 =21
t1= (-11-21)/2 = -32/2 = -16
t2 = (-11 +21)/2 = 10/2 =5
x^2 - 4x = -16
x^2 - 4x + 16 =0
D= 16-4*1*16= -48
D<0 нет корней<br>x^2 - 4x= 5
x^2 -4x -5 =0
D= 16 - 4*1*(-5) = 16+20 = 36 = 6^2
x1= (4 -6) /2 = -2/2 = -1
x2 = (4+6)/2 = 10/2 = 5