Răspuns:
Explicație pas cu pas:
[tex]a=\sqrt{26} -5,~b=\sqrt{6}+5,~daca~a*b=1,~rezulta~ca~b~este~inversul~lui~a.\\ a*b=(\sqrt{26} -5)*(\sqrt{26} +5)=(\sqrt{26})^{2} -5^{2}=26-25=1,~c.t.d.\\a^{2}-2\sqrt{26}*a+1=a*(a-2\sqrt{26})+1=(\sqrt{26} -5)*(\sqrt{26} -5-2\sqrt{26} )+1= (\sqrt{26} -5)*(-\sqrt{26} -5)+1=-(\sqrt{26} -5)*(\sqrt{26} +5)+1=-((\sqrt{26})^{2}-5^{2})+1=-(26-25)+1=-1+1=0[/tex]
