Polynomial Inequalities

Polynomial Inequalities Problem Solving


If x+y=20x+y=20, what is the maximum value of 2xy2xy?

A rectangular wall for a chicken coop is to be made out of a 44 m 44 \mbox{ m} wire mesh. Let xx be the shorter side of the rectangle in meters. If the area of the rectangle, AA, is 120 m2<A<121 m2 120 \mbox{ m}^2 < A < 121 \mbox{ m}^2, then xx must satisfy a<x<b a < x < b . What is the value of a+ba+b?

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

Which is larger?

Hint: Let x=22015 x = 2 ^ {2015} .

What is the maximum value of xx that satisfies the inequality (x6)(x24x+9)0 (x - 6)(x^2 - 4x + 9) \leq 0 ?


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