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[ 1/1Inequality]
Assignment:Find the solution set of inequality ln(1+1/x^1000)-(1+x^1000)^(1/1000)+x >= 0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
ln ( 1 + 1 / x ^ 1000 ) - ( 1 + x ^ 1000 ) ^ ( 1 / 1000 ) + x >= 0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of ln
1 + 1 / x ^ 1000 > 0 (3 )
From inequality(1)：
x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 70571/62500 或 70571/62500 ≤ x ≤ 302253/250000 或 302253/250000 ≤ x ≤ 58/45 或 58/45 ≤ x ≤ 273753/200000 或 273753/200000 ≤ x ≤ 724321/500000 或 724321/500000 ≤ x ≤ 1528519/1000000 或 1528519/1000000 ≤ x ≤ 321679/200000 或 321679/200000 ≤ x ≤ 105517/62500 或 x ≥ 105517/62500
From inequality(2)：
x < 0 或 x ＞ 0
From inequality(3)：
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequalities (1) and (2)
x < 0 或 0 < x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 70571/62500 或 70571/62500 ≤ x ≤ 302253/250000 或 302253/250000 ≤ x ≤ 58/45 或 58/45 ≤ x ≤ 273753/200000 或 273753/200000 ≤ x ≤ 724321/500000 或 724321/500000 ≤ x ≤ 1528519/1000000 或 1528519/1000000 ≤ x ≤ 321679/200000 或 321679/200000 ≤ x ≤ 105517/62500 或 x ≥ 105517/62500 (4)
From inequalities (3) and (4)
x < 0 或 0 < x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 70571/62500 或 70571/62500 ≤ x ≤ 302253/250000 或 302253/250000 ≤ x ≤ 58/45 或 58/45 ≤ x ≤ 273753/200000 或 273753/200000 ≤ x ≤ 724321/500000 或 724321/500000 ≤ x ≤ 1528519/1000000 或 1528519/1000000 ≤ x ≤ 321679/200000 或 321679/200000 ≤ x ≤ 105517/62500 或 x ≥ 105517/62500 (5)
The final solution set is :
x < 0 或 0 < x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 1049259/1000000 或 1049259/1000000 ≤ x ≤ 70571/62500 或 70571/62500 ≤ x ≤ 302253/250000 或 302253/250000 ≤ x ≤ 58/45 或 58/45 ≤ x ≤ 273753/200000 或 273753/200000 ≤ x ≤ 724321/500000 或 724321/500000 ≤ x ≤ 1528519/1000000 或 1528519/1000000 ≤ x ≤ 321679/200000 或 321679/200000 ≤ x ≤ 105517/62500 或 x ≥ 105517/62500Your problem has not been solved here? Please take a look at the hot problems ！
