Question

(x,y,z) merupakan solusi dari sistem persamaan (SP)
2/x + 1/y = 2
4/y +3/z = 5
3/x + 2/z = 3
nilai 1/x + 1/y + 1/z = ...

Answer 1

2/x + 1/y = 2 | x3
3/x + 2/z = 3 | x2

6/x + 3/y = 6
6/x + 4/z = 6
___________ -
3/y - 4/z = 0
3/y = 4/z
3*(4/3)/y = 4*(4/3)/z
4/y = (16/3)/z

4/y + 3/z = 5
(16/3)/z + 3/z = 5
(25/3)/z = 5
5z = 25/3
z = (25/3)/5
z = 5/3

3/y = 4/z
3/y = 4/(5/3)
3/y = 12/5
12y = 15
y = 15/12

2/x + 1/y = 2
2/x + 1/(15/12) = 2
2/x + 12/15 = 2
2/x = 2 - 12/15
2/x = 18/15
2.15 = 18x
15 = 9x
x = 15/9

jadi,

x = 15/9
y = 15/12
z = 5/3

1/x + 1/y + 1/z = 1/(15/9) + 1/(15/12) + 1/(5/3)
= 9/15 + 12/15 + 3/5
= 21/15 + 9/15
= 30/15
= 2