Question

解方程 x(x+1)(x²-2x-4)=0 x³-2x+1=0 x的4次方+8x³+14x²+8x+1=0

Answer 1

x(x+1)(x²-2x-4)=0
x1=0
x2=-1
x²-2x-4=0
x²-2x+1=5
(x-1)²=5
x3=1+√5
x4=1-√5

x³-2x+1=0
x³-x-x+1=0
x(x²-1)-(x-1)=0
x(x+1)(x-1)-(x-1)=0
(x²+x-1))(x-1)=0
x1=1
x²+x-1=0
x²+x+1/4=1+1/4
(x+1/2)²=5/4
x2=-1/2+√5/2
x3=-1/2-√5/2

x的4次方+8x³+14x²+8x+1=0
x^4+8x³+14x²+8x+1=0
x^4+x³+7x³+7x²+7x²+7x+x+1=0
x³(x+1)+7x²(x+1)+7x(x+1)+(x+1)=0
(x+1)(x³+7x²+7x+1)=0
x1=-1
x³+7x²+7x+1=0
x³+x²+6x²+6x+x+1=0
x²(x+1)+6x(x+1)+(x+1)=0
(x+1)(x²+6x+1)=0
x2=-1
x²+6x+1=0
x²+6x+9=9-1
(x+3)²=8
x3=-3+2√2
x4=-3-2√2

Answer 2

x(x+1)(x²-2x-4)=0
x1=0 x2=-1

x³-2x+1=0
x³-x-x+1=0
x(x^2-1)-(x-1)=0
x(x+1)(x-1)-(x-1)=0
(x^2+x-1))(x-1)=0
x=1

x^4+8x³+14x²+8x+1=0
x^4+8x^3+7x^2+7x^2+8x+1=0
x^2(x^2+8x+7)+(7x+1)(x+1)=0
x^2(x+7)(x+1)+(7x+1)(x+1)=0
(x^3+7x^2+7x+1)(x+1)=0
{(x^3+1)+7x(x+1)}(x+1)=0
(x+1)(x^2-x+1+7x)(x+1)=0
(x^2+7x+1)(x+1)^2=0
x=-1