Question 43
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, their product
is largest when they are equal. - If $a$ and $b$ are positive and unequal,
$\dfrac12(a^2+b^2)$ is greater than
$\left[\dfrac12(a+b)\right]^2.$ - If the product of two positive quantities is
given, their sum is greatest when they are equal.