Question

√5+√3/√5-√3=a+b√3 find the value of a and b​

Answer 1

$\huge{\bold{Answer:}}$

$\sf \frac{ \sqrt{5} + \sqrt{3}}{ \sqrt{5} - \sqrt{3} } = a + b \sqrt{3} \\ \\ \sf \frac{ \sqrt{5} + \sqrt{3}}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3}}{ \sqrt{5} + \sqrt{3} } \\ \\ \sf \frac{( \sqrt{5} + \sqrt{3}) {}^{2} }{( \sqrt{5} ) {}^{2} - ( \sqrt{3})^{2} } \\ \\ \sf \frac{( \sqrt{5}) {}^{2} + ( \sqrt{3}) {}^{2} - 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3} \\ \\ \sf \frac{5 + 3 - 2 \sqrt{15} }{2} \\ \\ \frac{8 - 2 \sqrt{15} }{2} \\ \\\sf \frac{ \cancel2(4 - \sqrt{15})}{ \cancel2} \\ \\ \bf 4 - 2 \sqrt{5 } * \sqrt{3 } = a + b \sqrt{3} \\ \\ \bf Therefore, \boxed{ \bf a = 4 \: and \: b = - 2 \sqrt{3}}$

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