Ta lấy [tex]5-\sqrt{26} -\left ( 4-\sqrt{17} \right )[/tex]
Nếu nó ra dương thì [tex]5-\sqrt{26}> 4-\sqrt{17}[/tex]
Còn nếu ra âm thì [tex]5-\sqrt{26}< 4-\sqrt{17}[/tex]
Ta có: [tex]5-\sqrt{26}-\left ( 4-\sqrt{17} \right )=5-\sqrt{26}-4+\sqrt{17}=1-\sqrt{26}+\sqrt{17}[/tex]
Ta lại có:[tex]-\sqrt{26}+\sqrt{17}> -\sqrt{25}+\sqrt{16}> -5+4> -1[/tex]
[tex]\Rightarrow -\sqrt{26}+\sqrt{17}+1> -\sqrt{25}+\sqrt{16}+1> 0[/tex]
[tex]\Rightarrow[/tex] Dương vậy [tex]5-\sqrt{26}> 4-\sqrt{17}[/tex]