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algebra senior

Problem

Of the following statements, the only one that is incorrect is:

(A)

An inequality will remain true after each side is increased,

decreased, multiplied or divided zero excluded by the same positive quantity.

(B)

The arithmetic mean of two unequal positive quantities is greater than their geometric mean.

(C)

If the sum of two positive quantities is given, ther product is largest when they are equal.

(D)

If a and b are positive and unequal, \frac{1}{2} (a^{2} + b^{2}) is greater than [\frac{1}{2} (a + b)]^{2} .

(E)

If the product of two positive quantities is given, their sum is greatest when they are equal.

Solution

The answer is

If the product of two positive quantities is given, their sum is greatest when they are equal.

. Quite the opposite of statement (E) is true--the sum

a + b

is minimized when

a = b

, but it approaches

\infty

when one of

a, b

gets arbitrarily small.

Final answer

E