[tex]\left(\sqrt{\sqrt2+1}-\sqrt{\sqrt2-1}\right)^2+\left(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5}\right)^2=[/tex]
[tex]=\sqrt2+1-2\sqrt{(\sqrt2-1)(\sqrt2+1)}+\sqrt2-1+3+\sqrt5+[/tex]
[tex]+\sqrt{(3-\sqrt5)(3+\sqrt5)}+3-\sqrt5=2\sqrt2-2+6+2=2\sqrt2+6[/tex]
Am folosit formulele:
[tex](a\pm b)^2=a^2\pm 2ab+b^2;\ \ (a-b)(a+b)=a^2-b^2;\ (\sqrt x)^2=x[/tex]