Respuesta :
Answer:
The value of ABC is 6.
Step-by-step explanation:
Consider the expression
[tex]\frac{1+\sqrt{3}}{1-\sqrt{3}}[/tex]
Rationalize the denominator.
[tex]\frac{1+\sqrt{3}}{1-\sqrt{3}}\times \frac{1+\sqrt{3}}{1+\sqrt{3}}[/tex]
[tex]\frac{(1+\sqrt{3})^2}{1^2-(\sqrt{3})^2}[/tex]
[tex]\frac{1^2+(\sqrt{3})^2+2\sqrt{3}}{1-3}[/tex]
[tex]\frac{1+3+2\sqrt{3}}{-2}[/tex]
[tex]\frac{4+2\sqrt{3}}{-2}[/tex]
[tex]\frac{4}{-2}+\frac{2\sqrt{3}}{-2}[/tex]
[tex]-2-\sqrt{3}[/tex] ..... (1)
The answer in the form
[tex]A+B\sqrt{C}[/tex] .... (2)
On comparing (1) and (2), we get
[tex]A=-2,B=-1,C=3[/tex]
We need to find the value of ABC.
[tex]ABC=(-2)(-1)(3)=6[/tex]
Therefore the value of ABC is 6.
