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This one is a bit tricky question ..
Value of root(2) = 1.414
since a is an integer and b is also an positive integer so ..
a/b is a rational number ..!
If a >b then a/b > 1
also value of a/b can be greater than 1.414 in some cases ...Like (2/1) ( so a>b can not be the option ...a must be less than b)
So condition is if a
Now (a+2b)/(a+b) can be written as 1 + b/(a+b)
So it is always greater than one ... Critically when a=b ..it will be equal to 1.5 which is greater than 1.414
But once a > b .. the value can fall less than 1.414 ..example 2 and 1 ...value will be 1.333
So Root(2) always lies between a/b and (a+2b)/(a+b) only if a ..
And i have shown above that ..how for a
Cheers :)
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