Упражнение№1
f := (sqrt(x+1)+sqrt(2*x))^2+7*(sqrt(x+1)-sqrt(2*x))^2 = 8;
solve(f, x);
Упражнение №3
restart; f := proc (x) options operator, arrow; x^3-(a+b+c)*x^2+(a*b+a*c+b*c)*x-a*b*c = 0 end proc; sol := {solve(f(x), x)}; nops(sol);
Упражнение №5
restart; f := 2*sqrt(x^2+x+4) = sqrt(3*x^2+5*x+9); sol := solve(f, x, explicit = true); simplify(mul(sol));
Упражнение №7
restart; f := {proc (x, y) options operator, arrow; 4/(x+y)+4/(x-y) = 3 end proc, proc (x, y) options operator, arrow; (x+y)^2+(x-y)^2 = 20 end proc}; sol := solve(f(x, y), {x, y}, explicit = true); map(rhs, map(op, [sol]));
Упражнение №9
restart; f := proc (x, y) options operator, arrow; x^2+y^2 = 8 end proc; g := proc (x, y) options operator, arrow; 2*x+2*y+x*y = 2 end proc; solve({f(x, y), g(x, y)}, {x, y}, explicit = true); plot([sqrt(-x^2+8), -sqrt(-x^2+8), (2-2*x)/(2+x)], x = -5 .. 5, y = -5 .. 5);
Упражнение №11
restart; f := x^2-2*a*(x-1)-1 = 0; sol := {solve(f, x)}; x1 := op(1, sol); x2 := op(2, sol); g := x1*x1+x2*x2 = x1+x2; solve(g, a);