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# Let x, a, b, c be nonnegative real numbers. Prove that

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Let x, a, b, c be nonnegative real numbers. Prove that

$$\left(x + \sqrt[3]{abc}\right)^3 \le (x + a)(x + b)(x + c) \le \left( x + \frac{a + b + c}{3} \right)^3.$$

Aug 19, 2020