Step 1 :Let's denote the amount invested at 1.7% as x, the amount invested at 2.3% as y, and the amount invested at 2.4% as z.
Step 2 :We know that the total amount invested was $26,000, which gives us the equation \(x + y + z = 26000\).
Step 3 :We also know that the amounts invested at 2.3% and 2.4% were equal, so we have \(y = z\).
Step 4 :The total annual interest earned was $598, which gives us another equation: \(0.017x + 0.023y + 0.024z = 598\).
Step 5 :We can solve these equations simultaneously to find the values of x, y, and z.
Step 6 :The solution to these equations is \(x = 2000\), \(y = 12000\), and \(z = 12000\).
Step 7 :So, the investor invested \(\boxed{2000}\) dollars at 1.7%, and \(\boxed{12000}\) dollars each at 2.3% and 2.4%.