Trivial Inequality: Difference between revisions
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==The Inequality== | |||
The trivial inequality states that <math>{x^2 \ge 0}</math> for all x. This is a rather useful inequality for proving that certain quantities are non-negative. The inequality appears to be obvious and unimportant, but it can be a very powerful problem solving technique. | The trivial inequality states that <math>{x^2 \ge 0}</math> for all x. This is a rather useful inequality for proving that certain quantities are non-negative. The inequality appears to be obvious and unimportant, but it can be a very powerful problem solving technique. | ||
==Applications== | |||
'''Maximizing and minimizing quadratic functions''' | '''Maximizing and minimizing quadratic functions''' | ||
After [[Completing the square]], the trivial inequality can be applied to determine the extrema of a quadratic function. | After [[Completing the square]], the trivial inequality can be applied to determine the extrema of a quadratic function. | ||
==Instructive National Math Olympiad Problem== | |||
<Anyone want to dig one up?> | |||
Revision as of 18:35, 17 June 2006
The Inequality
The trivial inequality states that 
for all x. This is a rather useful inequality for proving that certain quantities are non-negative. The inequality appears to be obvious and unimportant, but it can be a very powerful problem solving technique.
Applications
Maximizing and minimizing quadratic functions
After Completing the square, the trivial inequality can be applied to determine the extrema of a quadratic function.
Instructive National Math Olympiad Problem
<Anyone want to dig one up?>
