(1)已知a,b滿足-1≤a+b≤1,2≤a-b≤3試求3a-2b取值范圍(2)若正數x,y滿足xy=1+x+y,求x+y的大小(3)若z,b,c,d都為正數,則(a/b+c/d)(b/a+d/c)≥____謝謝大家了!!!!

熱心網友

(1):-1≤a+b≤1 ---(I)2≤a-b≤3 ---(II)[ (I)+(II) ]/2: 1/2 ≤a≤2 ---(III)(II)*2: 4≤2a-2b≤6 ---(IV)(III)+(IV): 9/2≤3a-2b≤8(2):xy=x+y+1≥2√xy+1 令√xy = t,t^2-2t-1≥0 t≥1+√2 或t≤1-√2（負數舍去）x+y=xy-1=t^2-1≥2+2√2(3):對于x,y0　有x+y≥2√xy故(a/b+c/d)(b/a+d/c)=1+ad/bc+bc/ad+1≥2+2=4

熱心網友

(1):-1≤a+b≤1 ---(I)2≤a-b≤3 ---(II)[ (I)+(II) ]/2: 1/2 ≤a≤2 ---(III)(II)*2: 4≤2a-2b≤6 ---(IV)(III)+(IV): 9/2≤3a-2b≤8(2):xy=x+y+1≥2√xy+1 令√xy = t,t^2-2t-1≥0 t≥1+√2 或t≤1-√2（負數舍去）x+y=xy-1=t^2-1≥2+2√2(3):對于x,y0　有x+y≥2√xy故(a/b+c/d)(b/a+d/c)=1+ad/bc+bc/ad+1≥2+2=4 很好了

熱心網友

我認為：(1)已知a,b滿足-1≤a+b≤1,2≤a-b≤3試求3a-2b取值范圍為（4+3b+2a≤3a-2b≤11+3b+2a）進一步簡化一下為：4≤a-5b≤11