Question

Diketahui a+b=8ab, b+c=12bc, dan a+c=16ac. Hitunglah a x b x c

Answer 1

A=6
b=2
c=10
maka a x b x c
=6x2x10
=120

Answer 2

a+b = 8ab <= bagi a semua

1 + b/a = 8b  <= bagi b semua

1/b + 1/a = 8 (1)

b+c = 12bc <= bagi b semua

1 + c/b = 12c <= bagi c semua

1/c + 1/b = 12  (2)

a+c = 16ac <= bagi a semua

1 + c/a = 16c <= bagi c semua

1/c + 1/a = 16 (3)

subtitusi : 1/a = x , 1/b = y , 1/c = z

y + x = 8  (1)

z + y = 12  (2)

z + x = 16  (3)

o z+x = 16

  z+y = 12

-------------- -

  x - y = 4  (4)

  y + x = 8

 ------------- +

  2x = 12

   x = 6

  1/a = 6

  a = 1/6

o z+x = 16

 z + 6 = 16

 z = 10

 1/c = 10

 c = 1/10

o z+y = 12

 10+y = 12

 y = 2

 1/b = 2

 b = 1/2

o a.b.c       = 1/6 . 1/2 . 1/10

                 = 1/12 . 1/10

a.b.c          = 1/120