已知数集\A={a+2,(a+1)2,a2+3a+3},B={a+b,1,a-b+5}.若A=B,求实数a,b的值
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![已知数集\A={a+2,(a+1)2,a2+3a+3},B={a+b,1,a-b+5}.若A=B,求实数a,b的值](/uploads/image/z/5439428-44-8.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E9%9B%86%5CA%3D%7Ba%2B2%2C%28a%2B1%292%2Ca2%2B3a%2B3%7D%2CB%3D%7Ba%2Bb%2C1%2Ca-b%2B5%7D.%E8%8B%A5A%3DB%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%2Cb%E7%9A%84%E5%80%BC)
已知数集\A={a+2,(a+1)2,a2+3a+3},B={a+b,1,a-b+5}.若A=B,求实数a,b的值
已知数集\A={a+2,(a+1)2,a2+3a+3},B={a+b,1,a-b+5}.若A=B,求实数a,b的值
已知数集\A={a+2,(a+1)2,a2+3a+3},B={a+b,1,a-b+5}.若A=B,求实数a,b的值
若a+2=1,则a=-1,于是a^2+3a+3=1,这与元素的互异性矛盾.
若(a+1)^2=1,则a=0或-2:
1)a=0时A={1,2,3},b=2,-b+5=3;或b=3,-b+5=2.
解得b=2或3.
2)a=-2时a^2+3a+3=1,这与元素互异性矛盾.
若a^2+3a+3=1,则a^2+3a+2=0,a≠-1,-2,无解.
综上,a=0,b=2或3.