Five Statements
Source:
February 1, 2009
inequalities
Problem Statement
Of the following statements, the only one that is incorrect is:
An inequality will remain true after each side is increased, decreased, multiplied or divided (zero excluded) by the same positive quantity.
The arithmetic mean of two unequal positive quantities is greater than their geometric mean.
If the sum of two positive quantities is given, ther product is largest when they are equal.
If and are positive and unequal, \frac {1}{2}(a^2 \plus{} b^2) is greater than [\frac {1}{2}(a \plus{} b)]^2.
If the product of two positive quantities is given, their sum is greatest when they are equal.