Di bantu jika a+b = 5ab, b+c = 3bc, dan a+c = 4ac, maka nilai a×b×c adalah a. 1/12 b. 1/6 c. 1/4 d. 1/3

jawab
a + b = 5 ab }bagi ab →1/a + 1/b = 5 ..(i)
b+ c = 3 bc  } bagi bc → 1/b + 1/c = 3..(ii)
a+c = 4ac  } bagi ac → 1/a + 1/c = 4..(iii)

(i) + (ii)
1/a + 1/b = 5
1/b + 1/c = 3 || (-)
1/a - 1/c = 2 ..(iv)

(iii) dan (iv)
1/a + 1/c = 4
1/a - 1/c = 2 ||  (+)
2/a = 6
1/a = 3

1/a + 1/c = 4
1/c = 4 -1/a
1/c = 4 - 3
1/c = 1

1/a + 1/b = 5
1/b = 5 - 1/a = 5 - 3
1/b = 2

(1/a)(1/b)(1/c) = 3(1)(2)
1/(abc) = 6/1
abc = 1/6

a+b=5ab => 1/a + 1/b=5...(i)
b+c=3bc => 1/a + 1/c=3...(ii)
a+c=4ac => 1/a + 1/c=4...(iii)
Dengan menggunakan metode eliminasi dari persamaan diatas,diperole nilai:
a=1/3
b=1/2
c=1
Maka a x b x c =1/3 x 1/2 x 1=(1x1x1)/(3x2)=1/6

Jawaban B