Question

If ab=1/4 and bc=1/3 and ac=1/3 then find a*b*c

Answer 1

`(1)/(6)`

Explanation:

Given

ab =
`(1)/(4)`

bc =
`(1)/(3)`

ac =
`(1)/(3)`

We will use the first equation to find b in terms of a.

b =
`(1)/(4a)`

Now we will substitute b into 2nd equation to find c in terms of a.

`((1)/(4a) )(c)=(1)/(3) \\(c)/(4a) =(1)/(3) \\3c = 4a\\c = (4a)/(3)`

Now we will substitute c into 3rd equation to find value a.

`a((4a)/(3) )=(1)/(3) \\(4a^(2) )/(3) =(1)/(3) \\4a^(2) =1\\a^(2) =(1)/(4) \\a=\sqrt{(1)/(4) } \\=(1)/(2)`

Now we will substitute a into first equation to find b.

b =
`(1)/(4((1)/(2)) ) \\=(1)/(2)`

Next we will substitute a into the 3rd equation to find c.

c =
`(4((1)/(2)) )/(3) \\=(2)/(3)`

Now we got all 3 values, when we multiply them together,

a x b x c =
`(1)/(2) *(1)/(2) *(2)/(3) \\=(2)/(12) \\=(1)/(6)`