Problem: If x+y=1x+y=1x+y=1, then the largest value of xyx yxy is:
Answer Choices:
A. 111
B. 0.50.50.5
C. an irrational number about 0.4
D. 0.250.250.25
E. 000 Solution:
If x+y=1x+y=1x+y=1, then P=xy=x(1−x)=−x2+xP=x y=x(1-x)=-x^{2}+xP=xy=x(1−x)=−x2+x. The largest value of PPP occurs when x=1/2x=1 / 2x=1/2.
∴P\therefore P∴P (maximum) =1/4=1 / 4=1/4.