申論題

4. Fix positive numbers a,b, c. For any (x, y, z) on the ellipsoid

x²/a² + y²/b² + z²/c² = 1 with x ＞ 0, y ＞0,z ＞0,

let A(x, y, z), B(x, y,z) and C(x, y, z) be the intercept that the tangent plane of the ellipsoid at (x,y, z) makes on the x-axis, the y-axis and the z-axis, respectively. Find the minimum of A(x,y, z) + B(x, y, z) +C(x,y, z).