已知集合A={x丨ax2-bx+3=0,x∈R}B={x丨x2-(b-1)x+2a=0,x∈R},若AnB={1},则AUB=

Question

已知集合A={x丨ax2-bx+3=0,x∈R} B={x丨x2-(b-1)x+2a=0,x∈R},若AnB={1},则AUB=

Answer 1

∵AnB={1} ∴x ＝1是两方程的解,带入后,得 a－b+3=0 2a －b+2=0 解得a ＝1 b＝4 带入原方程,得 A={x丨x－4x+3=0,x∈R} ＝ {x丨 ﹙ x－1 ﹚ ﹙x－3 ﹚ =0,x∈R} ＝ { 1,3 } B={x丨x－3x+2=0,x∈R} ＝ {x丨 ﹙ x－1﹚ ﹙ x－2 ﹚ =0,x∈R} ＝ { 1,2} AUB= { 1,2,3 }