设a1,a2,a3,a4,a5,为正整数,A={a1,a2,a3,a4,a5},B={a1²,a2²,a3²,a4²,a5²},且a1<a2<a3<+<a5,并满足A∩B={a1,a4},且a1+a4=10.求a1和a4的值,若A∪B 中各元素之和为256,求集合A.a1<a2<a3<a4<a5
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![设a1,a2,a3,a4,a5,为正整数,A={a1,a2,a3,a4,a5},B={a1²,a2²,a3²,a4²,a5²},且a1<a2<a3<+<a5,并满足A∩B={a1,a4},且a1+a4=10.求a1和a4的值,若A∪B 中各元素之和为256,求集合A.a1<a2<a3<a4<a5](/uploads/image/z/1581721-25-1.jpg?t=%E8%AE%BEa1%2Ca2%2Ca3%2Ca4%2Ca5%2C%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2CA%3D%7Ba1%2Ca2%2Ca3%2Ca4%2Ca5%7D%2CB%3D%7Ba1%26sup2%3B%2Ca2%26sup2%3B%2Ca3%26sup2%3B%2Ca4%26sup2%3B%2Ca5%26sup2%3B%7D%2C%E4%B8%94a1%EF%BC%9Ca2%EF%BC%9Ca3%EF%BC%9C%2B%EF%BC%9Ca5%2C%E5%B9%B6%E6%BB%A1%E8%B6%B3A%E2%88%A9B%3D%7Ba1%2Ca4%7D%2C%E4%B8%94a1%2Ba4%3D10.%E6%B1%82a1%E5%92%8Ca4%E7%9A%84%E5%80%BC%2C%E8%8B%A5A%E2%88%AAB+%E4%B8%AD%E5%90%84%E5%85%83%E7%B4%A0%E4%B9%8B%E5%92%8C%E4%B8%BA256%2C%E6%B1%82%E9%9B%86%E5%90%88A.a1%EF%BC%9Ca2%EF%BC%9Ca3%EF%BC%9Ca4%EF%BC%9Ca5)
设a1,a2,a3,a4,a5,为正整数,A={a1,a2,a3,a4,a5},B={a1²,a2²,a3²,a4²,a5²},且a1<a2<a3<+<a5,并满足A∩B={a1,a4},且a1+a4=10.求a1和a4的值,若A∪B 中各元素之和为256,求集合A.a1<a2<a3<a4<a5
设a1,a2,a3,a4,a5,为正整数,A={a1,a2,a3,a4,a5},B={a1²,a2²,a3²,a4²,a5²},且a1<a2<a3<+<a5,并满足A∩B={a1,a4},且a1+a4=10.求a1和a4的值,若A∪B 中各元素之和为256,求集合A.
a1<a2<a3<a4<a5
设a1,a2,a3,a4,a5,为正整数,A={a1,a2,a3,a4,a5},B={a1²,a2²,a3²,a4²,a5²},且a1<a2<a3<+<a5,并满足A∩B={a1,a4},且a1+a4=10.求a1和a4的值,若A∪B 中各元素之和为256,求集合A.a1<a2<a3<a4<a5
1.
因为a1,a4属于B,而B中的元素均为完全平方数,所以a1,a4,为完全平方数.
又因为0162,矛盾!所以a5
且a1<a2<a3<+<a5,
是什么意思??
因为a1< a2< a3< a4< a5 A∩B={a1, a4},
所以 A1^2=A1 A1=1
所以A4=9 所以9是B中一个元素 A4^2=81 所以只能 A2 或A3 的平方是9 假设A3=3 则A2只能是2 所以A={1,2,3,9,A5}B={1,4,9,81,A5^2} 所以有 A5^2+A5=256-110=146 A5非整数
假设A2=3 所以A5...
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因为a1< a2< a3< a4< a5 A∩B={a1, a4},
所以 A1^2=A1 A1=1
所以A4=9 所以9是B中一个元素 A4^2=81 所以只能 A2 或A3 的平方是9 假设A3=3 则A2只能是2 所以A={1,2,3,9,A5}B={1,4,9,81,A5^2} 所以有 A5^2+A5=256-110=146 A5非整数
假设A2=3 所以A5^2+A5>=100
A3^2+A3<=42 9>A3>2 所以A3=4,5,6
A3=6 A5=10
或{1,3,6,9,10}
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