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Question Number 144901 by loveineq last updated on 30/Jun/21

Let a,b > 0 and a+b+1 = 3ab. Prove that (a/(a^2 +1))+(b/(b^2 +1)) ≤ 1 ≤ (a^3 /(a^2 +1))+(b^3 /(b^2 +1)) Let a,b > 0, n ∈ Z^+ and a+b+1 = 3ab. Prove or disprove (a^(n−1) /(a^n +1))+(b^(n−1) /(b^n +1)) ≤ 1 ≤ (a^(n+1) /(a^n +1))+(b^(n+1) /(b^n +1))

Leta,b>0anda+b+1=3ab.Provethat aa2+1+bb2+1⩽1⩽a3a2+1+b3b2+1 Leta,b>0,n∈Z+anda+b+1=3ab.Proveordisprove an−1an+1+bn−1bn+1⩽1⩽an+1an+1+bn+1bn+1

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