11x²+8x+k=0; x₁ + 11x₂ = 2

11x²+8x+k=0| : 11;

x² + (8/11)x + k/11 = 0

По т. Виета x₁ + x₂ = -8/11 и x₁ · x₂ = k/11. Имеем x₁ + x₂ + 10x₂ = 2; -8/11 + 10x₂ = 2;

10x₂ = 2 + 8/11; 110x₂ = 22 + 8; x₂ = 30/110 = 3/11.

Отсюда x₁ + 3/11 = -8/11; x₁ = -8/11 - 3/11 = -11/11 = -1; k/11 = -1 · 3/11 = -3/11; k = -3.

Ответ: -3.