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Marina CMI [18]
3 years ago
7

Rationalize the denominator of \frac{1 \sqrt{3}}{1-\sqrt{3}}. When you write your answer in the form A B\sqrt{C}, where A, B, an

d C are integers, what is ABC?
Mathematics
1 answer:
kobusy [5.1K]3 years ago
7 0

Answer:

The value of ABC is 6.

Step-by-step explanation:

Consider the expression

\frac{1+\sqrt{3}}{1-\sqrt{3}}

Rationalize the denominator.

\frac{1+\sqrt{3}}{1-\sqrt{3}}\times \frac{1+\sqrt{3}}{1+\sqrt{3}}

\frac{(1+\sqrt{3})^2}{1^2-(\sqrt{3})^2}

\frac{1^2+(\sqrt{3})^2+2\sqrt{3}}{1-3}

\frac{1+3+2\sqrt{3}}{-2}

\frac{4+2\sqrt{3}}{-2}

\frac{4}{-2}+\frac{2\sqrt{3}}{-2}

-2-\sqrt{3}              ..... (1)

The answer in the form

A+B\sqrt{C}           .... (2)

On comparing (1) and (2), we get

A=-2,B=-1,C=3

We need to find the value of ABC.

ABC=(-2)(-1)(3)=6

Therefore the value of ABC is 6.

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