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Tag Archives: Inequality
Let be positive numbers other than such that . Prove that
The Engels form of the Cauchy – Schwartz inequality gives us:
and the inequality is proven.
Let be three positive real numbers such that . Prove that
By AM – GM we have,
Hence and the exercise is complete.
Let . Prove that
The LHS is equal to which by AM – GM is less or equal to
where . Since it follows from Bernoulli inequality that .
Let be positive real numbers such that . Prove that
Well if we apply AM-GM to we obtain
and similarly if we apply AM – GM to we obtain
We have successively,
Let be positive real numbers. Prove that
We apply the AM – GM inequality, thus:
Hence it suffices to prove that which holds because it is equivalent to .