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(1) \(a^2 < b^2\).. \(a^2<b^2\) means |a|<|b|.. Let us see what |a|<|b| tells us There can be two cases when |a|<|b| .. a) b is positive.... then b>a b) b is negative...then b<a.. These hold true irrespective of value of a It is given b>a ... Therefore, we can just say b is positive and nothing about a.. example.. a=2 and b=4, OR a=-2 and b=4.. Insufficient
(2) \(a^2 < ab < b^2\) \(a^2<ab......ab-a^2>0....a(b-a)>0\) Now, we know b-a>0 as b>a, therefore a>0... Since positive*positive>positive Sufficient