解不等式4x的3次方+6x的平方-2=>0 求詳解?
回答 (2)
2017-02-04 8:10 am
✔ 最佳答案
Sol4x^3+6x^2－2>=0
2x^3+3x^2－1>=0
(2x^3+x^2－x)+(2x^2+x－1)>=0
x(2x^2+x－1)+(2x^2+x－1)>=0
(x+1)(2x^2+x－1)>=0
(x+1)(2x－1)(x+1)>=0
(x+1)^2(2x－1)>=0
x=－1 or 2x－1>=0
x=－1 or x>=1/2
2017-02-04 12:19 am
4x³+6x²-2 ≧ 0
2(2x³+3x²-1) ≧ 0
2x³+3x²-1 ≧ 0
(2x³+2x²)+(x²-1) ≧ 0
2x²(x+1)+(x-1)(x+1) ≧ 0
(2x²+x-1)(x+1) ≧ 0
(2x-1)(x+1)(x+1) ≧ 0
(2x-1)(x+1)² ≧ 0
∵ (x+1)² ≧ 0 , ∴ 2x-1 ≧ 0
=> x+1 ≧ 0 和 2x-1 ≧ 0
=> x ≧ -1 和 2x ≧ 1
=> x ≧ -1 和 x ≧ 1/2
∴ x ≧ 1/2
2(2x³+3x²-1) ≧ 0
2x³+3x²-1 ≧ 0
(2x³+2x²)+(x²-1) ≧ 0
2x²(x+1)+(x-1)(x+1) ≧ 0
(2x²+x-1)(x+1) ≧ 0
(2x-1)(x+1)(x+1) ≧ 0
(2x-1)(x+1)² ≧ 0
∵ (x+1)² ≧ 0 , ∴ 2x-1 ≧ 0
=> x+1 ≧ 0 和 2x-1 ≧ 0
=> x ≧ -1 和 2x ≧ 1
=> x ≧ -1 和 x ≧ 1/2
∴ x ≧ 1/2
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