已知在x∈[m,n]时

C = | ( log₂ x )^2 + alog₂ x + (a/2)^2 + b - a^2/4 |= | (log₂ x + a/2 )^2+ b - a^2/4 |≤ 2 ；故当log₂ x = -a/2 时，C 有最小值-2；≤因此， -2 ≤ b - a^2/4≤2；(log₂ x + a/2 )^2 最大是(log₂ x + a/2 )^2 - 2 = 2，log₂ x + a/2≤2，log₂ x ≤2 + a/2，n = 2^( 2 + a/2 )；(log₂ x + a/2 )^2 最小是(log₂ x + a/2 )^2 + 2 = 2，log₂ x + a/2≤ 0，log₂ x ≤ a/2，m = 2^(a/2 )；故 n/m 最大值是2^( 2 + a/2 )/2^(a/2 ) = 4 。