已知集合a={y|y=x平方-二分之三x+1,x∈[3/4,2]},b={x|x+m平方≥1}命题p:x∈a,命题q：x∈B，

已知集合a={y|y=x平方-二分之三x+1,x∈[3/4,2]},b={x|x+m平方≥1}命题p:x∈a,命题q：x∈B，并且P是q的充分条件，求实数M。

需要具体过程

p:x∈[3/4,2] q:x≥1-m^2
P是q的充分条件，得p是q的子集 即1-m^2<=3/4，m>=1/2或m<= -1/2

y=x^2-(3/2)x+1=(x-3/4)^2+7/16 -1/2≤x≤2 -5/4≤x-3/4≤5/4 0≤(x-3/4)^2≤25/16 7/16≤(x-3/4)^2+7/16≤2 所以解集为[7/16，2] 易求得a=｛y|7/16≤y≤7/2｝b=｛x|x≥m＋1或者x≤m－1｝ ∵p是q的充分条件 ∴由p条件能得到条件q ∵p:x∈a,q:x∈b ∴a是b的子集 ∴7/16≥m＋1或者2≤m－1 解得m≥3或者m≤－9/16

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