Question

Positive numbers a, b, c, d satisfy `a^3 + b^3 +c ^3 + d^3 >= 3` and also `a^5 + b^5 +c ^5 + d^5 <= 5`

Prove that `a + b +c + d >= 3 / 2`

Difficulty level (1 very easy - 10 very hard): 5

Algebra -> Algebraic Techniques Algebra -> Inequalities -> Averages / Means

Sources:

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