please slove it as early as possible
x^1/2 + y = 7
x + y^1/2 = 11

prove that x = 9 and y = 4

• Let x^(1/2) = a and y^(1/2) = b
  Therefore, a + b² = 7 ---------- (1)
  a² + b = 11 ---------- (2)
  
  Multiply (1) by a² and Multiply (2) by a,
  
  a³ + a²b² = 7a² ---------- (1)
  a³ + ab = 11a ---------- (2)
  Subtract (1) and (2),
  
  a²b² – ab = 7a² – 11a
  -> ab(ab – 1) = a(7a – 11)
  -> b(ab – 1) = (7a – 11)
  -> ab² – b = 7a – 11
  -> – b = 7a – ab² – 11
  -> – b = a(7 – b²) – 11
  a = (11 – b)/(7 – b²)
  
  Let b = 1, 2,3,4 ...
  when b = 2
  a = (11 – b)/(7 – b²)
  = (11 – 2)/(7 – 4) = 9/3 = 3
  
  so a = 3 and b = 2 -> x^(1/2) = 3 and y^(1/2) = 2
  Hence x = 9 and y = 4
• 10 years agoHelpfull: Yes(1) No(2)
• Sorry @tark,
  but we cann't assume that a= --- and b= ---- now prove that
• 10 years agoHelpfull: Yes(0) No(0)