Mathematics: Is a multiple of a number is a power of the number?

The value of ABC is 6.Step-by-step explanation:Consider the expressionRationalize the denominator. ..... (1)The answer in the form .... (2)On comparing (1) and (2), we getWe need to find the value of ABC.Therefore the value of ABC is 6....

Is a multiple of a number is a power of the number?

Ответ:

morelos7078

30.07.2021

Mathematics

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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Is a multiple of a number is a power of the number?

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