lcm=16,8hcf(c,h,a,b)=1,2a-b=60a+b

解

l \cdot c \cdot m = 16, 8 h \cdot c \cdot f (c, h, a, b) = 1, 2 a - b = 60 a + b

(a = - \frac{b}{29}, b \in R, c = \frac{16}{l m}, h = \frac{l m}{128 f}, f \in R)

解答ステップ

l c m = 16 8 h c f = 1 2 a - b = 60 a + b

以下のために

c

を分離:

l \cdot c \cdot m = 16 : c = \frac{16}{l m}; l \neq = 0

以下に

c = \frac{16}{l m}

を挿入する:

8 h \cdot c \cdot f = 1

8 h \frac{16}{l m} f = 1

簡素化

\frac{128 h f}{l m} = 1

\frac{128 h f}{l m} = 1, 2 a - b = 60 a + b : a = - \frac{b}{29}, h = \frac{l m}{128 f}, f \neq = 0, l m \neq = 0

元のequationに当てはめて解を検算する

ゆえに,

l \cdot c \cdot m = 16, 8 h \cdot c \cdot f = 1, 2 a - b = 60 a + b

の最終的な解は

(a = - \frac{b}{29}, b \in R, c = \frac{16}{l m}, h = \frac{l m}{128 f}, f \in R)