Question

2+√3/2-√3=a+b√3 find a and b
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Answer 1

Answer:

• a = 7
• b = 4

Explanation:

Given,

$\implies \: \dfrac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3}$

Taking R. H. S. :-

$= \dfrac{2 + \sqrt{3} }{2 - \sqrt{3} }$

Rationalising the denominator,

$= \dfrac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \dfrac{2 + \sqrt{3} }{2 + \sqrt{3} }$

Using the identity :- (a - b)(a + b) = a² - b²

$= \dfrac{(2 + \sqrt{3} )(2 + \sqrt{3}) }{ {(2)}^{2} - {( \sqrt{3} )}^{2} }$

$= \dfrac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 - 3}$

$= \dfrac{7 + 4 \sqrt{3} }{1}$

$= 7 + 4 \sqrt{3}$

Now,

$\implies \: 7 + 4 \sqrt{3} = a + b\sqrt{3}$

On comparing,

$\therefore \: a = 7 \: { \rm \: and} \: b = 4$