Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Given
ab = [tex]\frac{1}{4}[/tex]
bc = [tex]\frac{1}{3}[/tex]
ac = [tex]\frac{1}{3}[/tex]
We will use the first equation to find b in terms of a.
b = [tex]\frac{1}{4a}[/tex]
Now we will substitute b into 2nd equation to find c in terms of a.
[tex](\frac{1}{4a} )(c)=\frac{1}{3} \\\frac{c}{4a} =\frac{1}{3} \\3c = 4a\\c = \frac{4a}{3}[/tex]
Now we will substitute c into 3rd equation to find value a.
[tex]a(\frac{4a}{3} )=\frac{1}{3} \\\frac{4a^{2} }{3} =\frac{1}{3} \\4a^{2} =1\\a^{2} =\frac{1}{4} \\a=\sqrt{\frac{1}{4} } \\=\frac{1}{2}[/tex]
Now we will substitute a into first equation to find b.
b = [tex]\frac{1}{4(\frac{1}{2}) } \\=\frac{1}{2}[/tex]
Next we will substitute a into the 3rd equation to find c.
c = [tex]\frac{4(\frac{1}{2}) }{3} \\=\frac{2}{3}[/tex]
Now we got all 3 values, when we multiply them together,
a x b x c = [tex]\frac{1}{2} *\frac{1}{2} *\frac{2}{3} \\=\frac{2}{12} \\=\frac{1}{6}[/tex]
