Simultaneous Equations

Question

Form a pair of simultaneous equations and solve them to find x and y, given that they are rational:

x-2y+√x+y (whole surd as in surd x+y, not just surd x) = 1/2√6

Answer 1

x-2y + √(x+y) = 1/(2√6) = 1/(2√6)[√6/√6]

 

x-2y + √(x+y) = √6/12 = √(6/144) = √(1/24)

 

Let x - 2y = 0

     x + y = 1/24

 

Subtract the equations to get -3y = -1/24

 

   So, y = 1/72 and x = 2y = 1/36