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
  
  Solving the quadratic equation r^2 = s^2, gives two roots for p i.e -3q and q/5
  As, -3q is not valid root only root is q/5.
• 12 years agoHelpfull: Yes(7) No(4)
• We can also use trail and error method.It is error free than equation solving method
• 11 years agoHelpfull: Yes(3) No(0)
• r = (3p + q) / 2 and s = (p - q)
  Then r² = [(3p + q) /2]² = (9p² + 6pq + q²) / 4
  And s² = (p - q)² = p² - 2pq + q²
  When r² = s² then, (9p² + 6pq + q²) / 4 = p² - 2pq + q²
  So, 9p² + 6pq + q² = 4p² - 8pq + 4q² : 5p² + 14pq - 3q² = 0
  Using the quadratic formula then p = [-14q ±√(196q² + 60q²)] ÷ 10 = (-14q ± 16q) / 10
  Then p = -30q/10 = -3q or p = 2q/10 = q/5
  ans : a
• 6 years agoHelpfull: Yes(2) No(0)