Question

Помогите пожалуйста!

Answer 1

$sqrt{6+2sqrt{5-sqrt{13+sqrt{48}}}}-sqrt{6-2sqrt{5+sqrt{13-sqrt{48}}}}=\\=[, 13pm sqrt{48}=1+12pm 2sqrt{12}=(1pm sqrt{12})^2, ]=\\=sqrt{6+2sqrt{5-sqrt{(1+sqrt{12})^2}}}-sqrt{6-2sqrt{5+sqrt{(1-sqrt{12})^2}}}=$

$=sqrt{6+2sqrt{5-(1+sqrt{12})}}}-sqrt{6-2sqrt{5+(sqrt{12}-1)}}}=\\=sqrt{6+2sqrt{4-sqrt{12}}}-sqrt{6-2sqrt{4+sqrt{12}}}=\\=sqrt{6+2sqrt{(1-sqrt3)^2}}-sqrt{6-2sqrt{(1+sqrt3)^2}}=$

$=sqrt{6+2(sqrt3-1)}-sqrt{6-2(1+sqrt3)}=\\=sqrt{4+2sqrt3}-sqrt{4-2sqrt3}=\\=sqrt{(1+sqrt3)^2}-sqrt{(1-sqrt3)^2}=|1+sqrt3|-|1-sqrt3|=\\=(1+sqrt3)-(sqrt3-1)=1+1=2$