Đáp án + giải thích các bước giải:
a) `\sqrt{2016}-\sqrt{2015}`
`=((\sqrt{2016}+\sqrt{2015})(\sqrt{2016}-\sqrt{2015}))/(\sqrt{2016}+\sqrt{2015})`
`=(2016-2015)/(\sqrt{2016}+\sqrt{2015})`
`=1/(\sqrt{2016}+\sqrt{2015})`
`\sqrt{2015}-\sqrt{2014}`
`=((\sqrt{2015}-\sqrt{2014})(\sqrt{2015}+\sqrt{2014}))/(\sqrt{2015}+\sqrt{2014})`
`=(2015-2014)/(\sqrt{2015}+\sqrt{2014})`
`=1/(\sqrt{2015}+\sqrt{2014})`
Vì `\sqrt{2016}>\sqrt{2014}`
`->\sqrt{2016}+\sqrt{2015}>\sqrt{2015}+\sqrt{2014}`
`->1/(\sqrt{2016}+\sqrt{2015})<1/(\sqrt{2015}+\sqrt{2014})`
`->\sqrt{2016}-\sqrt{2015}<\sqrt{2015}-\sqrt{2014}`
b) `(\sqrt{2015}+\sqrt{2017})^2`
`=2015+2017+2\sqrt{2015.2017}`
`=2016-1+2016+1+2\sqrt{(2016-1)(2016+1)}`
`=2.2016+2\sqrt{2016^2-1}`
`(2\sqrt{2016})^2=4.2016`
Vì `2\sqrt{2016^2-1}<2\sqrt{2016}^2`
`->2\sqrt{2016^2-1}<2.2016`
`->2.2016+2\sqrt{2016^2-1}<4.2016`
`->(\sqrt{2015}+\sqrt{2017})^2<(2\sqrt{2016})^2`
`->\sqrt{2015}+\sqrt{2017}<2\sqrt{2016}`
