Корен квадратен

[wenci]

Наредете числата [tex]a=\frac{9}{\sqrt{11}-\sqrt{2}}[/tex]; [tex]b=\frac{10}{2\sqrt{3}-\sqrt{2}}[/tex]

Опростете израза [tex]\sqrt{x^2-\sqrt{20}x+5}-\sqrt{x^2+\sqrt{20}x+5}[/tex] и пресметнете стойността му при
[tex]x=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}[/tex]

[Xixibg]

[tex]b=\sqrt{12}+\sqrt{2}>a=\sqrt{11}+\sqrt{2}[/tex]

[tex]x=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}\sqrt{2-\sqrt{2+\sqrt{3}}}[/tex]

[tex]x=\sqrt{2+\sqrt{3}}.\sqrt{(2+\sqrt{2+\sqrt{3}})(2-\sqrt{2+\sqrt{3}})}[/tex]

[tex]x=\sqrt{2+\sqrt{3}}.\sqrt{{4-2-\sqrt{3}[/tex]

[tex]x=\sqrt{2+\sqrt{3}}\sqrt{2-\sqrt{3}}[/tex]

[tex]x=4-3=1[/tex]

[tex]A=\sqrt{x^2-\sqrt{20}x+5}-\sqrt{x^2+\sqrt{20}x+5}[/tex]

[tex]A=\sqrt{(x-\sqrt{5})^2}-\sqrt{(x+\sqrt{5})^2}[/tex]

[tex]A=|x-\sqrt{5}|-|x+\sqrt{5}|[/tex]

[tex]A=\sqrt{5}-1-\sqrt{5}-1=-2[/tex]