Solve for x and y:
1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

• X= 3/2 and Y = 3
  1/x - 1/y = 1/3, 1/x^2 + 1/y^2 = 5/9.
  squaring both sides of 1/x - 1/y = 1/3 and substituting value of 1/x2 + 1/y2 = 5/9, we get 2/xy = 4/9.
  
  Find value of 1/x+1/y using formula (1/x+1/y)^2=(1/x - 1/y )^2 +4/xy
  Then
  1/x +1/y =1
  
  solving these , we get
  x= 3/2 and Y= 3
• 13 years agoHelpfull: Yes(9) No(3)
• x = 3/2 or -3 and y = 3 or -3/2.
  
  
  take 1/x=a, 1/y=b so, a-b=1/3, a2+b2=5/9, a2+b2=(a-b)2+2ab so, (a-b)2+2ab=5/9 (1/3)2+2ab=5/9 it gives ab=2/9 a=2/9b, so 2/9b-b=1/3 from this b=1/3 hence a=2/3 so x=3/2, y=3
  
• 8 years agoHelpfull: Yes(3) No(0)
• (a-b)^2 = a^2+b^2-2ab
  
  (1/x-1/y)^2= 1/x^2+1/y^2-2/xy
  
  we know 1/x^2+1/y^2 =5/9
  
  
  taking square root on both sides
  
  (1/x-1/y)^2 = (1/3)^2
  
  now you can simplify
• 10 years agoHelpfull: Yes(0) No(1)