20-05-09 greatest of smallest

x, y > 0 --> given
there can be four possible cases

1. x<1 y<1
here y+1/x>1 and 1/y>1 therefore s=x

2. x<1 y≥1
here s= x or 1/y depending on the values given to x and y

3. x≥1 y<1
same as above, s = x or 1/y

4. x≥1 y≥1
here s=1/y

among the four the s takes maximum value when s=1/y
the max value of s is 1
and y=1 and x ≥1

Not quite mrnobody :(

ans seems to be √2

Yes celestine