Classical topics of liberal arts mathematics in senior three.

Solution: When 1.a=5, the problem must be | x+ 1 |+x-2 |-5 ≥ 0. .......

Classification discussion:

1) when x

2) When-1≤x≤2, x+ 1≥0 and x-2≤0, ① the formula is (x+ 1)-(x-2)-5≥0, and there is no solution.

3)x & gt； 2 o'clock, x+1>; 0，x-2 & gt； 0, where the formula is (x+ 1)+(x-2)-5≥0, and x≥3 is obtained.

The domain of f(x) is (-∞, -2]U[3,+∞).

2. if f (x) = 0 has no solution, it must be | x+ 1 |+x-2 |-a > 0 to get a.

1) when x≤- 1, X+ 1 ≤ 0, X-2.

2) When-1

3) when x ≥ 2, x+1>; 0, x-2 ≥ 0, and ② is a.

To sum up, f(x)=0 has no solution to any X in the definition domain, and the range of real number A must be (-∞, 3).