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Kayasari Ryuunosuke Coordinator

07/08/2017 at 14:41
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Perfect :v 

***/ Give a,b,c > 0

Prove that : \(\dfrac{abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\le\dfrac{\left(a+b\right)\left(a+b+2c\right)}{\left(3a+3b+2c\right)^2}\le\dfrac{1}{8}\)

Source : Câu hỏi của Hoàng Phúc - Toán lớp 9 - Học toán với OnlineMath




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    AL 07/08/2017 at 17:02

    Use AM-GM's inequality we have:

    \(\dfrac{abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\le\dfrac{abc}{2\sqrt{ab}\cdot2\sqrt{bc}\cdot2\sqrt{ca}}\)\(=\dfrac{abc}{8abc}=\dfrac{1}{8}\)

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    Phan Huy Toàn 12/08/2017 at 15:07

    AL very good


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