Question

Rationalisation.

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2 - √3 / 2 + √3 = a - b√3

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Find value of a and b.


Thanks !☺☺☺

Answer 1

$\mathbb{\large{SOLUTION:}}$

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Given :

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$\mathsf{ \frac{2 -\sqrt{3} }{2 + \sqrt{3}} = a - b \sqrt{3}}$

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To find :

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Value of a and b.

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Main Solution :

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Solve the LHS by rationalising it's denominator.

2 - √3 / 2 + √3 = a - b√3

=> 2 - √3 / 2 + √3 × 2 - √3 / 2 - √3

=> ( 2 - √3 )² / (2)² - (√3)²

=> 4 + 3 - 4√3 / 4 - 3

=> 7 - 4√3

On comparing LHS with RHS, we get ;

$\mathsf{7 - 4 \sqrt{3} = a - b \sqrt{3}}$

Therefore,

Value of a = 7

Value of b = 4

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Thanks for the question !

Answer 2

Here is your solution

$\huge\boxed{\red{\bold{Given:-}}}$

$\frac{2 - \sqrt{3} }{2 + \sqrt{3} } = a - b \sqrt{3}$
$\underline{\purple{\bold{we\: have\: to\: find\: value\: of\: a\: and\: b\ }}}$

Now we rationalise

$= \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \frac{(2 - \sqrt{3} ) {}^{2} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ = \frac{4 + 3 - 2 \times 2 \times \sqrt{3} }{4 - 3} \\ \\ = \frac{7 - 4 \sqrt{3} }{1} \\ \\a - b \sqrt{3} = 7 - 4 \sqrt{3}$

The value of a and b

$\huge\underline{\pink{\bold{a=7}}}$
$\huge\underline{\pink{\bold{b=4}}}$

hope it helps you