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smc

algebra senior

Problem

If

x + y = 1

, then the largest value of

x y

is:

(A)

1

(B)

0.5

(C)

an irrational number about 0.4

(D)

0.25

Solution

By AM-GM, we have

\frac{x + y}{2} \geq x y

Substituting, we have

\frac{1}{2} \geq x y

\frac{1}{4} \geq x y

Equality occurs when

x = y = 0.25

.

Final answer

D