求解x^4-x^3-4x^2-2x

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求解x^4-x^3-4x^2-2x
求解x^4-x^3-4x^2-2x

求解x^4-x^3-4x^2-2x
x^4-x³-4x²-2x≦0
x^4-x³-2x²-2x²-2x≦0
x²(x²-x-2)-2x(x+1)≦0
x²(x-2)(x+1)-2x(x+1)≤0
x(x+1)[x(x-2)-2]≤0
x(x+1)(x²-2x-2)≤0
x(x+1)(x²-2x+1-3)≤0
x(x+1)[(x-1)²-3]≤0
1) x≤0 (1)
x+1≧0 则 x≥-1 (2)
(x-1)²-3≥0
(x-1)²≧3
x-1≥根号3 x≥1+根号3 (3)
x-1≤-根号3 x≤1-根号3 (4)
由（1）（2）（3）（4）可得
-1≤x≤1-根号3
2）x≤0 (1)
x+1≤0 则 x≤-1 (2)
(x-1)²-3≤0
(x-1)²≤3
-根号3≤x-1≤根号3
1-根号3≤x≤1+根号3 (3)
由（1）（2）（3）可得不等式无解
3) x≥0 (1)
x+1≤0 则 x≤-1 (2)
(x-1)²-3≥0
(x-1)²≧3
x-1≥根号3 x≥1+根号3 (3)
x-1≤-根号3 x≤1-根号3 (4)
由（1）（2）（3）（4）可得不等式无解
4) x≥0 (1)
x+1≥0 则 x≥-1 (2)
(x-1)²-3≤0
(x-1)²≤3
-根号3≤x-1≤根号3
1-根号3≤x≤1+根号3 (3)
由（1）（2）（3）可得
0≤x≤1+根号3

||是或的意思

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