Question

Simplify (1-√3)(1/3+√3) leaving your answer in form p+q√3

Answer 1

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Answer:

(1-√3)(1/3+√3)

1/3 +√3 -1/3*√3 -3

1/3 - 3 + √3 - 1/3*√3

1-9/3 +√3 - 1/3*√3

8/3 +√3 - 1/3*√3

8/3 + √3 ( 1-1/3 )

8/3 + √3 ( 3-1/2 )

8/3 + √3 *2/2

8/3 + 1√3

Here ,

p = 8/3

q = 1

Answer 2

p = $\frac{-8}{3}$  and q = $\frac{2}{3}$

Given:

(1-√3)(1/3+√3)

To Find:

To show it in the form of  p+q√3.

Solution:

(1-√3)(1/3+√3)

$=1\times \frac{1}{3} + 1 \times \sqrt{3} - \sqrt{3} \times \frac{1}{3} - \sqrt{3} \sqrt{3} \\\\= \frac{1}{3} +\sqrt{3} -\frac{\sqrt{3} }{3}-3\\\\ = \frac{1}{3}-3 +\sqrt{3} -\frac{\sqrt{3} }{3}\\\\= \frac{1-9}{3} + (1-\frac{1}{3})\sqrt{3} \\\\= \frac{-8}{3} +\frac{3-1}{3}\sqrt{3} \\\\= \frac{-8}{3} +\frac{2}{3}\sqrt{3}$

This is of the form p+q√3.Where p = $\frac{-8}{3}$  and q = $\frac{2}{3}$ .

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