Question

if a=5-√3÷5+√3 and b=5+√3÷5-√3 find a-b+2

Answer 1

$= > a = 5 - \sqrt{3} \div 5 + \sqrt{3} \\ \\ = > \: a = \frac{5 - \sqrt{3} }{5 + \sqrt{3} } \: \: \: \: .....[Eq_{1}]$
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$= > b = 5 + \sqrt{3} \div 5 - \sqrt{3} \\ \\ = > b = \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \: \: \: \: ...[Eq _{2}]$
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◢BY [Eq(1) - Eq(2)]

$= > a - b \: = \frac{5 - \sqrt{3} }{5 + \sqrt{3} } - \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ \\ = > a - b = \frac{ {(5 - \sqrt{3} )}^{2} - {(5 + \sqrt{3}) }^{2} }{(5 + \sqrt{3})(5 - \sqrt{3}) } \\ \\ = > a - b = \frac{(25 + 3 - 10 \sqrt{3} ) - (25 + 3 + 10 \sqrt{3} )}{( {5}^{2} - { \sqrt{3} }^{2}) } \\ \\ = > a - b = \frac{ - 20 \sqrt{3} }{25 - 3} = \frac{ - 20 \sqrt{3} }{22} \\ \\ = > a - b = - \frac{10 \sqrt{3} }{11} \\ \\ THEN \\ \\ = > a - b + 2 = - \frac{10 \sqrt{3} }{11} + 2 \\ \\ = > a - b + 2 = \frac{ - 10 \sqrt{3} + 22}{11} \\ \\ = > a - b + 2 = \frac{2( 11 - 5 \sqrt{3} ) }{11}$
____________________[◢ANSWER]

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