Polynomial Inequalities Problem Solving Practice Problems Online

If $x+y=20$ , what is the maximum value of $2xy$ ?

A rectangular wall for a chicken coop is to be made out of a $44 \mbox{ m}$ wire mesh. Let $x$ be the shorter side of the rectangle in meters. If the area of the rectangle, $A$ , is $120 \mbox{ m}^2 < A < 121 \mbox{ m}^2$ , then $x$ must satisfy $a < x < b$ . What is the value of $a+b$ ?

If $x$ and $y$ are positive numbers, what is the minimum value of $(3x + 4y)\left(\frac{27}{x} + \frac{4}{y} \right)$ ?

Which is larger?

Hint: Let $x = 2 ^ {2015}$ .

What is the maximum value of $x$ that satisfies the inequality $(x - 6)(x^2 - 4x + 9) \leq 0$ ?

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Polynomial Inequalities Problem Solving