(* zadacha 1 *)
((Sqrt[2+(Sqrt[3])])+(((2-2Cos[((11π)/6)]))^(1/2)))((((Sqrt[2+2Cos[(π/6)]])-(Sqrt[2+(Sqrt[3])])))^(-1))

((Sqrt[2+2Cos[(π/6)]])-(Sqrt[2+(Sqrt[3])])) (* delenie na 0 *)

(* zadacha 2 *)
f[x_]:=(x^2)-2(a+1)x-3(a^2);
Solve[f[x]==0,x]

ListLinePlot[Table[{1+a-(Sqrt[1+2 a+4 (a^2)]),1+a+(Sqrt[1+2 a+4 (a^2)])},{a,-5,5}]]

(* zadacha 3 *)
g[x_]:=(x^6)-14(x^4)+49(x^2)-36;
Factor[g[x]]

Apart[(1/(g[x]))]

(∑_(n=4)^∞)(1/(g[n]))

(* zadacha 4 *)
(* purvi nachin *)
Solve[7k+3t+11m==86 && 35k+15t+58m==442 && 1k+5==2m,{k,t,m}]

matrix={{7,3,11},{35,15,58},{1,0,-2}}

MatrixForm[matrix]

list={86,442,-5}

(* vtori nachin *)
LinearSolve[matrix,list]

inversematrix=Inverse[matrix]

(* treti nachin *)
inversematrix.list