Среднее арифметическое корней уравнения x * (x-3) ^3-x * (x-2) ^2 = 0

Выражение: x * (x-3) ^3-x * (x-2) ^2=0

Ответ: x^4-10*x^3+31*x^2-31*x=0

Решаем по действиям: 1. (x-3) ^3=x^3-9*x^2+27*x-27 (x-3) ^3 = ((x-3) * (x-3) * (x-3)) 1.1. (x-3) * (x-3) = x^2-6*x+9 (x-3) * (x-3) = x*x-x*3-3*x+3*3 1.1.1. x*x=x^2 x*x=x^ (1+1) 1.1.1.1. 1+1=2 + 1 _1_ 2 1.1.2. - x*3-3*x=-6*x 1.1.3. 3*3=9 X3 _3_ 9 1.2. (x^2-6*x+9) * (x-3) = x^3-9*x^2+27*x-27 (x^2-6*x+9) * (x-3) = x^2*x-x^2*3-6*x*x+6*x*3+9*x-9*3 1.2.1. x^2*x=x^3 x^2*x=x^ (2+1) 1.2.1.1. 2+1=3 + 2 _1_ 3 1.2.2. x*x=x^2 x*x=x^ (1+1) 1.2.2.1. 1+1=2 + 1 _1_ 2 1.2.3. - x^2*3-6*x^2=-9*x^2 1.2.4. 6*3=18 X6 _3_ 18 1.2.5. 18*x+9*x=27*x 1.2.6. 9*3=27 X9 _3_ 272. x * (x^3-9*x^2+27*x-27) = x^4-x^3*9+x^2*27-x*27 x * (x^3-9*x^2+27*x-27) = x*x^3-x*9*x^2+x*27*x-x*27 2.1. x*x^3=x^4 x*x^3=x^ (1+3) 2.1.1. 1+3=4 + 1 _3_ 4 2.2. x*x^2=x^3 x*x^2=x^ (1+2) 2.2.1. 1+2=3 + 1 _2_ 3 2.3. x*x=x^2 x*x=x^ (1+1) 2.3.1. 1+1=2 + 1 _1_ 23. (x-2) ^2=x^2-4*x+4 (x-2) ^2 = ((x-2) * (x-2)) 3.1. (x-2) * (x-2) = x^2-4*x+4 (x-2) * (x-2) = x*x-x*2-2*x+2*2 3.1.1. x*x=x^2 x*x=x^ (1+1) 3.1.1.1. 1+1=2 + 1 _1_ 2 3.1.2. - x*2-2*x=-4*x 3.1.3. 2*2=4 X2 _2_ 44. x * (x^2-4*x+4) = x^3-x^2*4+x*4 x * (x^2-4*x+4) = x*x^2-x*4*x+x*4 4.1. x*x^2=x^3 x*x^2=x^ (1+2) 4.1.1. 1+2=3 + 1 _2_ 3 4.2. x*x=x^2 x*x=x^ (1+1) 4.2.1. 1+1=2 + 1 _1_ 25. x^4-x^3*9+x^2*27-x*27 - (x^3-x^2*4+x*4) = x^4-x^3*9+x^2*27-x*27-x^3+x^2*4-x*46. - x^3*9-x^3=-10*x^37. x^2*27+x^2*4=31*x^28. - x*27-x*4=-31*x

Решаем по шагам: 1. x * (x^3-9*x^2+27*x-27) - x * (x-2) ^2=0 1.1. (x-3) ^3=x^3-9*x^2+27*x-27 (x-3) ^3 = ((x-3) * (x-3) * (x-3)) 1.1.1. (x-3) * (x-3) = x^2-6*x+9 (x-3) * (x-3) = x*x-x*3-3*x+3*3 1.1.1.1. x*x=x^2 x*x=x^ (1+1) 1.1.1.1.1. 1+1=2 + 1 _1_ 2 1.1.1.2. - x*3-3*x=-6*x 1.1.1.3. 3*3=9 X3 _3_ 9 1.1.2. (x^2-6*x+9) * (x-3) = x^3-9*x^2+27*x-27 (x^2-6*x+9) * (x-3) = x^2*x-x^2*3-6*x*x+6*x*3+9*x-9*3 1.1.2.1. x^2*x=x^3 x^2*x=x^ (2+1) 1.1.2.1.1. 2+1=3 + 2 _1_ 3 1.1.2.2. x*x=x^2 x*x=x^ (1+1) 1.1.2.2.1. 1+1=2 + 1 _1_ 2 1.1.2.3. - x^2*3-6*x^2=-9*x^2 1.1.2.4. 6*3=18 X6 _3_ 18 1.1.2.5. 18*x+9*x=27*x 1.1.2.6. 9*3=27 X9 _3_ 272. x^4-x^3*9+x^2*27-x*27-x * (x-2) ^2=0 2.1. x * (x^3-9*x^2+27*x-27) = x^4-x^3*9+x^2*27-x*27 x * (x^3-9*x^2+27*x-27) = x*x^3-x*9*x^2+x*27*x-x*27 2.1.1. x*x^3=x^4 x*x^3=x^ (1+3) 2.1.1.1. 1+3=4 + 1 _3_ 4 2.1.2. x*x^2=x^3 x*x^2=x^ (1+2) 2.1.2.1. 1+2=3 + 1 _2_ 3 2.1.3. x*x=x^2 x*x=x^ (1+1) 2.1.3.1. 1+1=2 + 1 _1_ 23. x^4-x^3*9+x^2*27-x*27-x * (x^2-4*x+4) = 0 3.1. (x-2) ^2=x^2-4*x+4 (x-2) ^2 = ((x-2) * (x-2)) 3.1.1. (x-2) * (x-2) = x^2-4*x+4 (x-2) * (x-2) = x*x-x*2-2*x+2*2 3.1.1.1. x*x=x^2 x*x=x^ (1+1) 3.1.1.1.1. 1+1=2 + 1 _1_ 2 3.1.1.2. - x*2-2*x=-4*x 3.1.1.3. 2*2=4 X2 _2_ 44. x^4-x^3*9+x^2*27-x*27 - (x^3-x^2*4+x*4) = 0 4.1. x * (x^2-4*x+4) = x^3-x^2*4+x*4 x * (x^2-4*x+4) = x*x^2-x*4*x+x*4 4.1.1. x*x^2=x^3 x*x^2=x^ (1+2) 4.1.1.1. 1+2=3 + 1 _2_ 3 4.1.2. x*x=x^2 x*x=x^ (1+1) 4.1.2.1. 1+1=2 + 1 _1_ 25. x^4-x^3*9+x^2*27-x*27-x^3+x^2*4-x*4=0 5.1. x^4-x^3*9+x^2*27-x*27 - (x^3-x^2*4+x*4) = x^4-x^3*9+x^2*27-x*27-x^3+x^2*4-x*46. x^4-10*x^3+x^2*27-x*27+x^2*4-x*4=0 6.1. - x^3*9-x^3=-10*x^37. x^4-10*x^3+31*x^2-x*27-x*4=0 7.1. x^2*27+x^2*4=31*x^28. x^4-10*x^3+31*x^2-31*x=0 8.1. - x*27-x*4=-31*x

Решаем уравнение x^4-10*x^3+31*x^2-31*x=0: Тестовая функция, правильность не гарантируется Не можем решить.