Question

If a=root5 - root3/root5 + root3 and b=root5 + root3/root5 - root3 find a+b+ab

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$a = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ b = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ a + b + ab \\ = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } + \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + (\frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } ) \\ = \frac{ {( \sqrt{5} - \sqrt{3} )}^{2} + {( \sqrt{5} + \sqrt{3} )}^{2} }{( \sqrt{5} + \sqrt{3})( \sqrt{5} - \sqrt{ 3} )} \times \frac{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3} )}{( \sqrt{5} + \sqrt{3} )( \sqrt{5} - \sqrt{3})} \\ = \frac{5 - 2 \sqrt{5} \sqrt{3} - 3 + 5 + 2 \sqrt{5} \sqrt{3} + 3 }{ { (\sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \times 1 \\ = \frac{5 +5}{5 - 3} = \frac{10}{2} = 5$