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
Follow Math Help Forum on Facebook and Google+
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
View Tag Cloud