Thread: inequalities

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

For the example assume a = 0 so b>0



which is false

Originally Posted by rmpatel5

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

........................eqn(1)

Multiply both sides with a, we get,

.....................eqn(2)

Now multiply both sides of eqn(1) with b, we get

...................eqn (3)

from eqn(2) and eqn (3)

Multiply both sides by
since can be 0

Multiply both sides by


Hence

A counter example for is given by 11rdc11