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Question Number 205767 by lmcp1203 last updated on 30/Mar/24

  a,b,c ∈ℜ^+     a+b+c=1     a^2 /(1+b+c) + b^2 /(1+a+c)  + c^2 /(1+a+b)≥k  find   k max.  hint : inequality cauchy schwarz

a,b,c+a+b+c=1a2/(1+b+c)+b2/(1+a+c)+c2/(1+a+b)kfindkmax.hint:inequalitycauchyschwarz

Answered by A5T last updated on 30/Mar/24

Σ(a^2 /(1+b+c))≥(((a+b+c)^2 )/(3+2(a+b+c)))=(1/5)

Σa21+b+c(a+b+c)23+2(a+b+c)=15

Commented by lmcp1203 last updated on 30/Mar/24

thanks

thanks

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