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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