设全集u={2,3,a²+2a-3},A={2a-1|,2},CuA={5},则实数a等于?
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![设全集u={2,3,a²+2a-3},A={2a-1|,2},CuA={5},则实数a等于?](/uploads/image/z/2692582-70-2.jpg?t=%E8%AE%BE%E5%85%A8%E9%9B%86u%3D%7B2%2C3%2Ca%26%23178%3B%2B2a-3%7D%2CA%3D%EF%BD%9B2a-1%EF%BD%9C%2C2%7D%2CCuA%3D%7B5%7D%2C%E5%88%99%E5%AE%9E%E6%95%B0a%E7%AD%89%E4%BA%8E%3F)
设全集u={2,3,a²+2a-3},A={2a-1|,2},CuA={5},则实数a等于?
设全集u={2,3,a²+2a-3},A={2a-1|,2},CuA={5},则实数a等于?
设全集u={2,3,a²+2a-3},A={2a-1|,2},CuA={5},则实数a等于?
因为CuA={5},
即A={2,3}
而全集u={2,3,a²+2a-3},
所以
a²+2a-3=5
a²+2a-8=0
(a-2)(a+4)=0
a=2或a=-4
从而
|2a-1|=3
a=2时成立,(a=-4时,左边=9不行,)
所以
a=2.
2a-1=3
a²+2a-3=5
∴a=2
因为CuA={5},所以,a²+2a-3=5.
a=-4或2