Question

rationalize the demominater and find the value of a&b
$\frac{2 + \sqrt{3} }{2 - \sqrt{3 } } = a + b \sqrt{3}$
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Answer 1

Answer

a = 7 and b = 4

EXPLANATION.

TO FIND THE VALUE OF A AND B.

$\bold{ \longrightarrow{ \frac{2 \: + \sqrt{3} }{2 \: - \: \sqrt{3} } } = \: a \: + \: b \sqrt{3}}$

Rationalize the term

$\bold{\longrightarrow{ \frac{2 \: + \: \sqrt{3} }{2 \: - \: \sqrt{3} } } \times \: \frac{2 \: + \: \sqrt{3} }{2 \: + \: \sqrt{3} } }$

$\bold{\implies{ \frac{(2 + \sqrt{3}) {}^{2} }{(2 \: - \: \sqrt{3})(2 \: + \: \sqrt{3}) }} }$

$\bold{\implies{ \frac{4 \: + \: 3 \: + \: 4 \sqrt{3} }{4 \: - \: 3} }}$

$\bold{\implies{ \frac{7 \: + \: 4 \sqrt{3} }{1} } = a \: + \: b \sqrt{3}}$

Therefore,

value of a = 7

value of b = 4