i have a problem to prove this.. Let a,b,c be positive real numbers such that abc=1, prove that 1/(a^3*(b+c))+1/(b^3*(c+a))+1/(c^3*(a+b))>=3/2. can anyone solve this problem? thank you
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Let The inequality becomes By Cauchy-Schwarz or
Since both sides positives since the assumption is given, so the LHS is Now apply Cauchy–Schwarz and get Hence since we have our inequality.
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