Question

已知不等式,①X²-4X﹢3＜0,②.X²-6X﹢8＜0,③.2X²-9X﹢M＜0,若同时

Answer 1

①x²-4x+3＜0

(x-1)(x-3)＜0

则1＜x＜3

②x²-6x+8＜0

(x-2)(x-4)＜0

则2＜x＜4

同时满足①②的x是2＜x＜3满足③2x²-9x+M＜0

令f(x)=2x²-9x+M

则f(2)≤0,f(3)≤0

所以8-18+M≤0,18-18+M≤0

所以M≤10,M≤0

故M≤0