Question

Express 1-1/1+root 3 + 1/1- root 3 in the form of a + b root 3

Answer 1

Step-by-step explanation:

Given:

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

To find:

Express in the form of

$a + \sqrt{3} b$

Solution:

First take LCM

$1 - \frac{1}{1 + \sqrt{3} } + \frac{1}{1 - \sqrt{3} } \\\\=>\frac{(1 + \sqrt{3})(1 - \sqrt{3} ) - ( 1 - \sqrt{3} ) + 1 + \sqrt{3} }{(1 + \sqrt{3})(1 - \sqrt{3} ) } \\ \\= > \frac{(1 - ( { \sqrt{3}) }^{2} ) - ( 1 - \sqrt{3} ) + 1 + \sqrt{3} }{(1 + \sqrt{3})(1 - \sqrt{3} ) } \\ \\ \because \: (x - y)(x + y) = {x}^{2} - {y}^{2} \\ \\ = > \frac{1 - 3 - 1 + \sqrt{3} + 1 + \sqrt{3} }{(1 + \sqrt{3})(1 - \sqrt{3} ) } \\ \\ = > \frac{ - 2 + 2 \sqrt{3} }{1 - ( { \sqrt{3} )}^{2} } \\ \\ = > \frac{ - 2(1 - \sqrt{3} )}{ - 2} \\ \\ = > 1 - \sqrt{3} \\ \\ a + b \sqrt{3} = 1 - \sqrt{3}$

Thus,

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

can be expressed as

$1 - \sqrt{3}$

in form of

$a + b \sqrt{3}$

Hope it helps you.

To learn more on brainly:

1)Rationalise the denominator of : 5/√3-√5

https://brainly.in/question/2676020

2)Rationalise the denominator of 1/√5+√2.

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Answer 2

Answer:

can be expressed as 1-√3