Equation gives the eprd for a general binary system as

Question

Equation gives the EPRD for a general binary system as σ = L₁₁X₁₂ + 2L₁₂X₁X₂ + L₂₂X₂₂ > 0. This quadratic form has to be positive for all positive or negative values of X₁ and X₂. Show that this requires that

a. L₁₁ > 0.

b. L₂₂ > 0.

c. L₁₁L₂₂ > 2L₁₂.

σ_total = Σ^m_i=1 j_iX_i = Σ^m_i=1 Σ^m_j=1 L_ijX_jX_i > 0