# Having trouble with Solve [closed]

I am unable to solve the following system of equations using Solve.

Solve[
{1[E^(-i (k1 + k2)) (1 + E^(i (k1 + k2))) (E^(2 i k2) x + E^(2 i k1) y)] ==
2 (-1 + Cos[k1] + Cos[k2])[E^(i k2) x + E^(i k1) y],
2 ((-(1/2))
[E^(-i (k1 - 2 k2)) x + E^(2 i k1 - i k2) y + E^(3 i k2) (x + y)] +
(Cos[k1] + Cos[k2])[E^(2 i k2) x + E^(2 i k1) y]) ==
1[(1 + E^(i (k1 + k2))) (E^(i k2) x + E^(I k1) y)]},
{x, y}]

• If MMA cannot solve it, I'm not sure what you expect us to do. Solvable equations are the exception, not the rule. – AccidentalFourierTransform Jul 11 '19 at 13:52
• You have two problems: need upper case I for imaginary i and you can't use brackets to enclose expressions. Use parentheses. Make those changes and try it. – Dominic Jul 11 '19 at 14:21
• Some clarification: Use parenthesis to enclose expressions but brackets for function arguments like (a+b Cos[a]) and double brackets for array indexing like myArray[[index]]. – Dominic Jul 11 '19 at 14:29
• Hi user66523, welcome to Mma.SE. Start by taking the tour now and learning about asking and what's on-topic. Your question was put on-hold as it seems to be off-topic, i.e it arises from a simple mistake (syntax error) and will not help future visitors. Don't be discouraged by that cleaning-up policy. Your future good questions are welcome. Learn about common pitfalls here. Why not choosing a meaningful username? – rhermans Jul 11 '19 at 16:09

Replace i with I and some [] with () and simplify to see what we have.

Simplify[{1(E^(-I (k1 + k2)) (1 + E^(I (k1 + k2))) (E^(2 I k2) x + E^(2 I k1) y)) ==
2 (-1 + Cos[k1] + Cos[k2])(E^(I k2) x + E^(I k1) y),
2 ((-(1/2))(E^(-I (k1 - 2 k2)) x + E^(2 I k1 - I k2) y + E^(3 I k2) (x + y)) +
(Cos[k1] + Cos[k2])(E^(2 I k2) x + E^(2 I k1) y)) == ((1 + E^(I (k1 + k2)))*
(E^(I k2) x + E^(I k1) y))}]

(*{(1 - 2*E^(I*k2) + E^(I*(k1 + k2)))*x + (1 - 2*E^(I*k1) + E^(I*(k1 + k2)))*y == 0,
E^((3*I)*k1)*y == E^((3*I)*k2)*y}*)


Now try to solve

Solve[%,{x,y}]

(*{{x->0,y->0}}*)
`

Using Reduce instead of Solve will show a much longer result with various possible conditions on some expressions which may or may not hold in your situation. If some of those conditions hold then there are other potential solutions.