Question

solve step by step
b) 2+√3÷2-√3

Answer 1

Heya !!!



2 + ✓3 / 2 - ✓3


Rationalizing the denominator 2-✓3


=> 2+✓3/ 2- ✓3 × ( 2 + ✓3) / ( 2+✓3)



=> ( 2 + ✓3) ( 2+✓3) / ( 2-✓3) ( 2+✓3)



=> (2)² + (✓3)² + 2 × 2 × ✓3 / (2)² - (✓3)²



=> 4 + 3 + 4✓3 / 4 - 3



=> 7+4✓3 /1


=> 7+4✓3....ANS....



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Answer 2

Using the Identities :

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ (a + b)(a - b) = {a}^{2} - {b}^{2}$

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

On rationalizing the denominator we get,

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