Problem: The polynomial (x+y)9 is expanded in decreasing powers of x. The second and third terms have equal value when evaluated at x=p and y=q, where p and q are positive numbers whose sum is one. What is the value of p?
Answer Choices:
A. 1/5
B. 4/5
C. 1/4
D. 3/4
E. 8/9
Solution:
(x+y)9=x9+9x8y+36x7y2+⋯+y9;
9p8q=36p7q2 and p+q=1;
p=4q and p+q=1;p=4/5.