已知M(x,y) A(0,-1/2) B(-1,0)三点共线 则2^x+4^y的最小值为
人气:485 ℃ 时间:2020-05-19 02:23:16
解答
向量AM=(x,y+1/2)
向量BM=(x+1,y)
而M(x,y) A(0,-1/2) B(-1,0)三点共线
所以(x+1)(y+1/2)=xy
所以得 x/2+y+1/2=0
x+2y=-1
而2^x+4^y=2^x+2^(2y)>=2√(2^x*2^(2y))=2√2^(x+2y)=2√(1/2)=√2
所以最小值为√2
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