将y = x + m带入x²/4 + y²/2 = 1:3x² + 4mx + 2(m² - 2) = 0
x₁ + x₂ = -4m/3
x₁x₂ = 2(m² - 2)/3
|AB|² = (x₁ - x₂)² + (y₁ - y₂)² = (x₁ - x₂)² + (x₁ + m - x₂ - m)² = 2(x₁ - x₂)² = 2[(x₁ + x₂)² -4x₁x₂] = 2[16m²/9 - 8(m² - 2)/3]
= 16(6 - m²)/9
m = 0时,|AB|²最大,|AB| = 4√6/3