Вычислить 2 cos 2П/5+cos4п/5+cos6П/5

   1. Применим формулу для суммы косинусов:

• x = 2cos(2π/5) + cos(4π/5) + cos(6π/5);
• x = 2cos(2π/5) + 2cos(π)cos(π/5);
• x = 2(cos(2π/5) - cos(π/5)). (1)

   2. Возведем в квадрат уравнение (1), с учетом того, что x < 0:

• x^2 = 4(cos(2π/5) - cos(π/5))^2;
• x^2 = 4(cos^2(2π/5) - 2cos(2π/5)cos(π/5) + cos^2(π/5));
• x^2 = 2(1 + cos(4π/5)) - 4(cos(3π/5) + cos(π/5)) + 2(1 + cos(2π/5));
• x^2 = 2 - 2cos(π/5) + 4(cos(2π/5) - cos(π/5)) + 2 + 2cos(2π/5);
• x^2 = 4 + 6(cos(2π/5)- cos(π/5));
• x^2 = 4 + 3x;
• x^2 - 3x - 4 = 0;

• D = 3^2 + 4 * 4 = 9 + 16 = 25;
• x = (3 ± √25)/2 = (3 ± 5)/2;

• x1 = (3 - 5)/2 = -2/2 = -1;
• x2 = (3 + 5)/2 = 8/2 = 4, не подходит.

   Ответ: -1.