`a)`
`N=( 1+( a+\sqrt{a})/(\sqrt{a}+1)).(1-(a-\sqrt{a})/(\sqrt{a}-1))` `(a≥0;a\ne1)`
`=(1+(\sqrt{a}(\sqrt{a}+1))/(\sqrt{a}+1)).(1-(\sqrt{a}(\sqrt{a}-1))/(\sqrt{a}-1))`
`=(1+\sqrt{a})(1-\sqrt{a})`
`=1-a`
`b)`
`Để` `N < -1`
`⇔1-a<-1`
`⇔-a<-1-1`
`⇔-a<-2`
`⇔a>2`
`Vậy.....`
`c)`
`Để` `N=\sqrt{a}-5`
`⇔1-a=\sqrt{a}-5`
`⇔-a-\sqrt{a}+5+1=0`
`⇔-a-3\sqrt{a}+2\sqrt{a}+6=0`
`⇔-\sqrt{a}(\sqrt{a}+3)+2(\sqrt{a}+3)=0`
`⇔(\sqrt{a}+3)(-\sqrt{a}+2)=0`
`⇔` \(\left[ \begin{array}{l}\sqrt{a}+3=0\\-\sqrt{a}+2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}\sqrt{a}=-3(VN)\\-\sqrt{a}=-2\end{array} \right.\)
`⇔ \sqrt{a}=2`
`⇔a=4` `(tm)`
`Vậy.....`
