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(1)已知a,b满足-1≤a+b≤1,2≤a-b≤3试求3a-2b取值范围(2)若正数x,y满足xy=1+x+y,求x+y的大小(3)若z,b,c,d都为正数,则(a/b+c/d)(b/a+d/c)≥____谢谢大家了!!!!

热心网友

(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（负数舍去）x+y=xy-1=t^2-1≥2+2√2(3):对于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

热心网友

(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（负数舍去）x+y=xy-1=t^2-1≥2+2√2(3):对于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

热心网友

我认为：(1)已知a,b满足-1≤a+b≤1,2≤a-b≤3试求3a-2b取值范围为（4+3b+2a≤3a-2b≤11+3b+2a）进一步简化一下为：4≤a-5b≤11