Question

$\sqrt{5} + \sqrt{3} \div \sqrt{5} - \sqrt{3} = a + b \sqrt{15}$
find out a and b​

Answer 1

Answer:

a = 4 , b = 1

Step-by-step explanation:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{ 3} } \: = a + b \sqrt{15} \\ = \frac{( \sqrt{5} + \sqrt{3} ) ( \sqrt{5} + \sqrt{3} )}{( \sqrt{5} - \sqrt{3} ) ( \sqrt{5} + \sqrt{3}) } \\ = \frac{ {( \sqrt{5} + \sqrt{3} )}^{2} }{ { (\sqrt{5} )}^{2} - {( \sqrt{3}) }^{2} } \\ = \frac{ {( \sqrt{5} )}^{2} + {( \sqrt{3}) }^{2} + 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3} \\ = \frac{5 + 3 + 2 \sqrt{15} }{2} \\ = \frac{8 + 2 \sqrt{15} }{2} \\ = 4 + \sqrt{15}$

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Answer 2

Answer:

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