If r = (3p + q)/2 and s = p – q, for which of the following values of p would r^2 = s^2 ?
b) 10 - (3/2q)
c) q - 1
e) (9/2q) - 9
I got A.
Solve for p when r^2=s^2, which is same as [(3p+q)/2]^2 = (p-q)^2
--> (9p^2+6pq+q^2)/4 = p^2-2pq+q^2 *multiply 4 on both sides*
--> 9p^2+6pq+q^2 = 4p^2-8pq+4q^2 *simplify*
--> 5p^2+14pq-3q^2=0 *factor*
--> (5p-q)*(p+3q)=0 *solve*
--> p=q/5 OR p=-3q
Since -3q isn't in one of the answer choices, the answer must be A.