Next year, my father (repair) ________________the house.
Q = |x + 1| + |x - 2015| = |x + 1| + |2015 - x| >= |x + 1 + 2015 - x| = |2016| = 2016
Q = 2016 <=> (x + 1)(2015 - x) >= 0
Cho x + 1 = 0 => x = -1
2015 - x = 0 => x = 2015
Ta có bảng xét dấu:
x | -1 2015 |
x + 1 | - 0 + | + |
2015 - x | + | + 0 - |
(x + 1)(2015 - x) | - 0 + 0 - |
=> -1 <= x <= 2015
Vậy: Qmin = 2016 <=> -1 <= x <= 2015