已知a>0,b>0,a+b=2;则y=1/a+4/b的最小值是多少啊?

Question

已知a>0,b>0,a+b=2;则y=1/a+4/b的最小值是多少啊?

Answer 1

把a+b=2代入,得,y=1/a+4/b
=(a+b)/2a+2(a+b)/b
=1/2+b/2a+2+2a/b
=5/2+b/2a+2a/b
≥5/2+2×根下b/2a×2a/b
=9/2 ,当且仅当b²=4a²取到.