Найдите сумму корней, с решением

Question

Найдите сумму корней, с решением

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Comments

(x-1)²(x-2)² -3(x-1)(x-2) -(x-2) =0 ;(x-2)((x-1)²(x-2) -3(x-1) -1) =0 ;(x-2)(x³ -4x² +2x) =0 ;x(x-2)(x² -4x+2) =0 ; * * * D/4 =2 >0 * * *x₁ +x₂ +(x₃ +x₄) = 0+2 +4 =6.

Answer 1

x^4 + 9x² + 4 - 6x³ + 4x² - 12x - 3x² + 9x - 6 + 2 - x = 0
x^4 - 6x³ + 10x² - 4x = 0
x(x³-6x²+10x-4)=0
x1 = 0
x³ - 6x² + 10x - 4 = 0
(x³ - 2x²) - (4x² - 8x )+ (2x - 4 )= 0
x²(x-2)-4x(x-2)+2(x-2)=0
(x - 2)(x² - 4x + 2) = 0
x2 = 2
x² - 4x + 2 = 0
D=16-8=8
x3 = (4-2√2)/2=2 - √2
x4 = (4+2√2)/2=2 + √2
x1+x2+x3+x4=0+2+2-√2+2+√2=6

Answer 2

Раскрываем скобки
(x^2 - 3x + 2)^2 - 3(x^2 - 3x + 2) + 2 - x = 0
x^4 + 9x^2 + 4 - 6x^3 + 4x^2 - 12x - 3x^2 + 9x - 6 + 2 - x = 0
x^4 - 6x^3 + 10x^2 - 4x = 0
x1 = 0
x^3 - 6x^2 + 10x - 4 = 0
x^3 - 2x^2 - 4x^2 + 8x + 2x - 4 = 0
(x - 2)(x^2 - 4x + 2) = 0
x2 = 2
x^2 - 4x + 2 = 0
D/4 = 4 - 2 = 2
x3 = 2 - √2
x4 = 2 + √2
Сумма корней x1 + x2 + x3 + x4 = 0 + 2 + 2 - √2 + 2 + √2 = 6