0≤a<b, prove that a^2≤ab<b^2. Also, show by example that it does not follow that a^2<ab<b^2

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- September 10th 2008, 07:35 PMrmpatel5inequalities
0≤a<b, prove that a^2≤ab<b^2. Also, show by example that it does not follow that a^2<ab<b^2

- September 10th 2008, 07:42 PM11rdc11
For the example assume a = 0 so b>0

which is false - September 10th 2008, 07:58 PMShyam
- September 10th 2008, 08:57 PMacc100jt
Multiply both sides by

since can be 0

Multiply both sides by

Hence

A counter example for is given by 11rdc11