Find two numbers whose difference is 2 and whose AM exceeds the GM by 1/2. 

x+y/2  - root of xy =1/2

x - y =2

x = 2 + y

2+y+y /2 -root of 2y + y2=1/2

1+y -root of  2y + y2 = 1/2

1/2 + y = root of 2y + y2

squaring on both side

(1/2 +y )2  =2y + y2

1/4 + y2 +y = 2y + y2

1/4 = 2y - y

y = 1/4

and x =2 +y

  x= 2 + 1/4

   x = 9 /4

thats the answer

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If the A.M between a and b is twice their G.M. then prove that a:b=(2+sqrt3):(2-sqrt3)
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