Question

[bui manh dung]

cho a,b,c >0, a+b=1 CMR

a, \(\frac{1}{ab}+\frac{1}{a^2+b^2}>=6\)

cac ban oi giup minh di. minh dang can gap

Answer 1

[Nguyễn Nhật Minh]

\(\frac{1}{ab}+\frac{1}{a^2+b^2}=\frac{2}{2ab}+\frac{1}{a^2+b^2}\ge\frac{\left(\sqrt{2}+1\right)^2}{2ab+a^2+b^2}=\frac{3+2\sqrt{2}}{\left(a+b\right)^2}=3+2\sqrt{2}\)

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