ALjabar

Misal :

1/(x + 2) = a

1/(y + 1) = b

1/(z - 1) = c

soal

(1) -4a + 4b + 9c = -6 → -8a + 8b + 18c = -12

(2) 8a + 6b + 3c = 4

(3) 4a + 2b - 6c = 2 → 8a + 4b - 12c = 4

persamaan (1) dan (2)

-8a + 8b + 18c = -12

8a + 6b + 3c = 4___(+)

14b + 21c = -8 ... (4)

pers (2) dan (3)

8a + 6b + 3c = 4

8a + 4b - 12c = 4_(-)

2b + 15c = 0

b = -15/2 c ... (5)

pers (4) dan (5)

14b + 21c = -8

14(-15/2)c + 21c = -8

-105c + 21c = -8

-84c = -8

c = 8/84

c = 2/21

1/(z - 1) = 2/21

z - 1 = 21/2

z = 23/2

b = -15/2 c

b = -15/2 × 2/21

b = -5/7

1/(y + 1) = -5/7

y + 1 = -7/5

y = -12/5

pers (3)

4a + 2b - 6c = 2

2a + b - 3c = 1

2a - 5/7 - 2/7 = 1

2a - 7/7 = 1

a = 1

1/(x + 2) = 1

x = -1

HP (x,y,z) = {(-1 , -12/5 , 23/2)}