Solve[equation, vars]Solve[equation, vars, domain]Complexes or Reals or Integers.Solve[x ^ 2 - 3 x == 4, x]
Solve[4 y - 8 == 0, y]
Apply the solution:
sol = Solve[2 x^2 - 10 x - 12 == 0, x]
x /. sol
Contradiction:
Solve[x + 1 == x, x]
Tautology:
Solve[x ^ 2 == x ^ 2, x]
Rational equations:
Solve[x / (x ^ 2 + 1) == 1, x]
Solve[(x^2 + 3 x + 2)/(4 x - 2) == 0, x]
Transcendental equations:
Solve[Cos[x] == 0, x]
Solve can only solve equations with respect to symbols or functions:
Solve[f[x + y] == 3, f[x + y]]
Solve[a + b == 2, a + b]
This happens when solving with respect to an assigned symbol:
x = 3;
Solve[x == 2, x]
Clear[x]
Solve[a < b, a]
Solve a system of equations:
eqs = {3 x ^ 2 - 3 y == 0, 3 y ^ 2 - 3 x == 0};
sol = Solve[eqs, {x, y}] // Simplify
eqs /. sol // Simplify
Solve when given an underdetermined system:
Solve[x^2 == 1 && z^2 == -1, {x, y, z}]
Examples using specifying the Domain in solutions:
Solve[x^2 == -1, x, Reals]
Solve[x^2 == 1, x, Reals]
Solve[x^2 == -1, x, Complexes]
Solve[4 - 4 * x^2 - x^4 + x^6 == 0, x, Integers]