Answer:
P₁(1/9; 1/72)
P₂(1/10; 1/40)
P₃(1/12; 1/24)
P₄(1/16; 1/16)
Step-by-step explanation:
(1/m) + (1/n) = 1/8
(m+n)/(m*n) = 1/8
8*(m+n) = m*n
8m + 8n = m*n
8m – m*n = -8n
m (8-n) = -8n
m = 8n / (n-8)
If
n = 9
m = 8*9 / (9-8) = 72
then
(1/72) + (1/9) = 1/8
If
n = 10
m = 8*10 / (10-8) = 40
then
(1/40) + (1/10) = 1/8
If
n = 12
m = 8*12 / (12-8) = 24
then
(1/24) + (1/12) = 1/8
If
n = 16
m = 8*16 / (16-8) = 16
then
(1/16) + (1/16) = 1/8
Finally, the pairs of positive unit fractions that add up to 1/8 are
P₁(1/9; 1/72)
P₂(1/10; 1/40)
P₃(1/12; 1/24)
P₄(1/16; 1/16)
