请写出过程:
设a>2 ,b>3, c>6> 令M=abc , N=ab+ac+bc
则M,N的大小关系为( )。
过年了,祝大家羊年如意!
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N = ab + ac + bc
= abc/c + abc/b + abc/a
= M/c + M/b + M/a
= M*(1/c +1/b + 1/a)
∵ a>2 => 1/a < 1/2
b>3 => 1/b < 1/3
c>6 => 1/c < 1/6
∴ N = M*(1/c +1/b + 1/a) < M*(1/2 + 1/3 +1/6) = M
结论:N < M
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up
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:)
来晚了