I.
[latex]left[sqrt{6- sqrt{11}} + sqrt{6- sqrt{11}}
ight]^{2}=[/latex]
[latex]left[2sqrt{6- sqrt{11}}
ight]^{2}=[/latex]
[latex]4(6- sqrt{11})=24-4 sqrt{11}[/latex]
gdyby w pod drugim pierwiastkiem był + zamiast -, wtedy
[latex][ sqrt{6- sqrt{11}} + sqrt{6+sqrt{11}} ] ^{2}=[/latex]
[latex]6- sqrt{11} +2 cdot sqrt{6- sqrt{11}} cdot sqrt{6+ sqrt{11}}+6- sqrt{11}=[/latex]
[latex]12 +2 cdot sqrt{(6- sqrt{11})cdot (6+sqrt{11})}}=12 +2 cdot sqrt{36-11}=[/latex]
[latex]12 +2 cdot sqrt{25}=12+2 cdot 5=12+10=22[/latex]
==========================
II.
[latex]sqrt{9- 4sqrt{5}} - sqrt{9+4 sqrt{5}}=[/latex]
[latex]sqrt{ 5-4sqrt{5}+4} - sqrt{5+4sqrt{5}+4}=[/latex]
[latex]sqrt{( sqrt{5} )^2-4sqrt{5}+2^2} -sqrt{( sqrt{5} )^2+4sqrt{5}+2^2}=[/latex]
[latex]sqrt{( sqrt{5} -2)^2} -sqrt{( sqrt{5}+2)^2}=[/latex]
[latex]|sqrt{5} -2| -|sqrt{5}+2|=[/latex]
[latex]sqrt{5} -2 -sqrt{5}-2=-4 in W[/latex]
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[latex]sqrt{21+ 4sqrt{5}} + sqrt{14-6 sqrt{5}}=[/latex]
[latex]sqrt{20+ 4sqrt{5}+1} + sqrt{9-6 sqrt{5}+5}=[/latex]
[latex]sqrt{( sqrt{20} )^2+ 4sqrt{5}+1^2} + sqrt{3^2-6 sqrt{5}+( sqrt{5} )^2}=[/latex]
[latex]sqrt{( sqrt{20}+1)^2} + sqrt{(3-sqrt{5} )^2}=[/latex]
[latex]|sqrt{20}+1| + |3-sqrt{5} |=[/latex]
[latex]2sqrt{5}+1 + 3-sqrt{5}=sqrt{5}+4in IW[/latex]
