1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B含于A,求实数x的取值范围.3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a-6a+10},A含于M,且A含于N,求
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![1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B含于A,求实数x的取值范围.3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a-6a+10},A含于M,且A含于N,求](/uploads/image/z/2713201-25-1.jpg?t=1.%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%EF%BD%9Ba%2Ca%2Bb%2Ca%2Bb%26%23178%3B+%EF%BD%9D%2CB%3D%EF%BD%9Ba%2Cax%2Cax%26%23178%3B%EF%BD%9D%2CA%3DB%2C%E6%B1%82x%E7%9A%84%E5%80%BC.2.%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7Bx%EF%BD%9C-2%E2%89%A4x%E2%89%A45%7D%2CB%3D%7Bx%EF%BD%9Cm%2B1%E2%89%A4x%E2%89%A42m%2B1%7D.B%E5%90%AB%E4%BA%8EA%2C%E6%B1%82%E5%AE%9E%E6%95%B0x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.3.%E5%B7%B2%E7%9F%A5A%3D%EF%BD%9B2%2C3%EF%BD%9D%2CM%3D%7B2%2C5%2Ca%26%23178%3B-3a%2B5%7D%2CN%3D%7B1%2C3%2Ca-6a%2B10%7D%2CA%E5%90%AB%E4%BA%8EM%2C%E4%B8%94A%E5%90%AB%E4%BA%8EN%2C%E6%B1%82)
1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B含于A,求实数x的取值范围.3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a-6a+10},A含于M,且A含于N,求
1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.
2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B含于A,求实数x的取值范围.
3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a-6a+10},A含于M,且A含于N,求实数a的值.
1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B含于A,求实数x的取值范围.3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a-6a+10},A含于M,且A含于N,求
1.已知集合A={a,a+b,a+b² },B={a,ax,ax²},A=B,求x的值.
由a+b=ax,得 x=1+(b/a) .(1)
由a+b²=ax²,得x²=1+(b²/a).(2)
故有 [1+(b/a)]²=1+(b²/a),化简得 2b/a+(b²/a²)=b²/a,去分母得2ab+b²=ab²,∵b≠0,可消去b
得2a+b=ab,∴b=2a/(a-1),代入(1)式便得x=1+2/(a-1)=(a+1)/(a-1)
此时x²=(a+1)²/(a-1)²,于是ax=a(a+1)/(a-1),ax²=a(a+1)²/(a-1)²,
a+b=a+2a/(a-1)=(a²-a+2a)/(a-1)=a(a+1)/(a-1)=ax
a+b²=a+4a²/(a-1)²=[a(a-1)²+4a²]/(a-1)²=a(a+1)²/(a-1)²=ax²
故有A=B
2.已知集合A={x|-2≤x≤5},B={x|m+1≤x≤2m+1}.B⊆A,求实数x的取值范围.
m+1≧-2,得m≧-3;2m+1≦5,得m≦2;故-3≦m≦2.
3.已知A={2,3},M={2,5,a²-3a+5},N={1,3,a²-6a+10},A⊂M,且A⊂N,求实数a的值.
由a²-3a+5=3,得a²-3a+2=(a-2)(a-1)=0,故a=1或2.(1);
由a²-6a+10=2,得a²-6a+8=(a-2)(a-40=0,故a=2或4.(2);
(1)∩(2)={a︱a=2}
此时,M={2,5,3};N={1,3,2}.
哈哈。不好意思,我不怎么会第一个问题应该是:X等于(a+b*b)/(a+b)或者/(a+b)/(a+b*b).当然还要考虑分母是不是零的情况!