Prove that $fraca2a+beta b+fracbalpha b+beta age frac2alpha +beta $

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Let $a;b;alpha;beta>0$ and $beta>alpha $. Prove that $$fraca2a+beta b+fracbalpha b+beta age frac2alpha +beta $$



$$LHS-RHS=fraca^2alpha beta+a^2beta^2-4a^2beta+abalpha^2+abalphabeta-2abalpha-2abbeta^2+2abbeta-b^2alphabeta+b^2beta^2(alpha +beta)(2a+beta b)(alpha b+beta a) ge0$$



Then i can not solve it, help me !




proof-verification inequality examples-counterexamples fractions




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    Let $a;b;alpha;beta>0$ and $beta>alpha $. Prove that $$fraca2a+beta b+fracbalpha b+beta age frac2alpha +beta $$



    $$LHS-RHS=fraca^2alpha beta+a^2beta^2-4a^2beta+abalpha^2+abalphabeta-2abalpha-2abbeta^2+2abbeta-b^2alphabeta+b^2beta^2(alpha +beta)(2a+beta b)(alpha b+beta a) ge0$$



    Then i can not solve it, help me !




    proof-verification inequality examples-counterexamples fractions




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Let $a;b;alpha;beta>0$ and $beta>alpha $. Prove that $$fraca2a+beta b+fracbalpha b+beta age frac2alpha +beta $$



      $$LHS-RHS=fraca^2alpha beta+a^2beta^2-4a^2beta+abalpha^2+abalphabeta-2abalpha-2abbeta^2+2abbeta-b^2alphabeta+b^2beta^2(alpha +beta)(2a+beta b)(alpha b+beta a) ge0$$



      Then i can not solve it, help me !




      proof-verification inequality examples-counterexamples fractions




      share|cite|improve this question













      Let $a;b;alpha;beta>0$ and $beta>alpha $. Prove that $$fraca2a+beta b+fracbalpha b+beta age frac2alpha +beta $$



      $$LHS-RHS=fraca^2alpha beta+a^2beta^2-4a^2beta+abalpha^2+abalphabeta-2abalpha-2abbeta^2+2abbeta-b^2alphabeta+b^2beta^2(alpha +beta)(2a+beta b)(alpha b+beta a) ge0$$



      Then i can not solve it, help me !





      proof-verification inequality examples-counterexamples fractions





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      share|cite|improve this question




      share|cite|improve this question








      edited yesterday









      Michael Rozenberg

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      asked yesterday









      Nguyễn Duy Linh

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          It's wrong.



          Try $beta=1$, $alpha=frac12$ and $a=b=1.$






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          active

          oldest

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          up vote
          1
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          accepted










          It's wrong.



          Try $beta=1$, $alpha=frac12$ and $a=b=1.$






          share|cite|improve this answer

















          • 1




            Can you delete this question ?
            – Nguyễn Duy Linh
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          up vote
          1
          down vote



          accepted










          It's wrong.



          Try $beta=1$, $alpha=frac12$ and $a=b=1.$






          share|cite|improve this answer

















          • 1




            Can you delete this question ?
            – Nguyễn Duy Linh
            yesterday












          up vote
          1
          down vote



          accepted







          up vote
          1
          down vote



          accepted






          It's wrong.



          Try $beta=1$, $alpha=frac12$ and $a=b=1.$






          share|cite|improve this answer













          It's wrong.



          Try $beta=1$, $alpha=frac12$ and $a=b=1.$







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered yesterday









          Michael Rozenberg

          86.9k1575178




          86.9k1575178







          • 1




            Can you delete this question ?
            – Nguyễn Duy Linh
            yesterday












          • 1




            Can you delete this question ?
            – Nguyễn Duy Linh
            yesterday







          1




          1




          Can you delete this question ?
          – Nguyễn Duy Linh
          yesterday




          Can you delete this question ?
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