UPDATE: THIS this "PROOF" IS proof" is WRONG. !
We want to prove that a^(2-2a)+(1-a)^(2a)<=1 for 0<=a<=1, or for 0<=a<=1/2 because of symmetry under a -> 1-a. Set f(a)=a^(2-2a). Then we want to prove that f(a)<=1-f(1-a), but since trivially f(a)<=a in [0,1/2], we have f(a)<=a<=1-a<=1-f(1-a). QED
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UPDATE: THIS "PROOF" IS WRONG. We want to prove that a^(2-2a)+(1-a)^(2a)<=1 for 0<=a<=1, or for 0<=a<=1/2 because of symmetry under a -> 1-a. Set f(a)=a^(2-2a). Then we want to prove that f(a)<=1-f(1-a), but since trivially f(a)<=a in [0,1/2], we have f(a)<=a<=1-a<=1-f(1-a). QED |
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We want to prove that a^(2-2a)+(1-a)^(2a)<=1 for 0<=a<=1, or for 0<=a<=1/2 because of symmetry under a -> 1-a. Set f(a)=a^(2-2a). Then we want to prove that f(a)<=1-f(1-a), but since trivially f(a)<=a in [0,1/2], we have f(a)<=a<=1-a<=1-f(1-a). QED |
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