If r = (3p + q)/2 and s = p - q, for which of the following values of p would r2 = s2?
A. 1q/5
B. 10 - 3q/2
C. q - 1
D. 3q
E. 9q/2 - 9
A. 1q/5
B. 10 - 3q/2
C. q - 1
D. 3q
E. 9q/2 - 9
r^2 = s^2
=> (3p + q)^2 / 4 = (p-q)^2
=> 9p^2 + 6pq +q^2 = 4p^2 - 8pq + 4q^2
=> 5p^2 +14pq - 3q^2 = 0
=> 5p^2 + 15pq - pq - 3q^2 = 0
=> 5p(p+3q) - q(p-3q) = 0
=> (5p - q)*(p-3q) = 0
=> p = q/5 OR p = 3q
Pick D
I'm not sure what A is, but I think you may have mistyped it?
EDIT: The equation should be (5p - q)*(p + 3q) MY BAD! Thanks selango!
