已知正整数a,b满足4a+b=30,使得1/a+1/b取最小值时,则实数对(a,b)是

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已知正整数a,b满足4a+b=30,使得1/a+1/b取最小值时,则实数对(a,b)是

已知正整数a,b满足4a+b=30,使得1/a+1/b取最小值时,则实数对(a,b)是
已知正整数a,b满足4a+b=30,使得1/a+1/b取最小值时,则实数对(a,b)是

已知正整数a,b满足4a+b=30,使得1/a+1/b取最小值时,则实数对(a,b)是
因为4a+b=30 1/a+1/b=(1/a+1/b)(4a+b)/30 =(b/a+4a/b+5)/30 ∵b/a+4a/b>=4,当且仅当b/a=4a/b ∴b/a=4a/b→b=2a 所以,4a+b=6a=30 解得,a=5,b=2a=10 ∴实数对(a,b)=(5,10)