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D e a r s t u d e n t, a . \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} \times \frac{7 - 4 \sqrt{3}}{7 - 4 \sqrt{3}} = \frac{(5 + 2 \sqrt{3}) (7 - 4 \sqrt{3})}{(7^{2} - {(4 \sqrt{3})}^{2})} = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} = \frac{11 - 6 \sqrt{3}}{1} = 11 - 6 \sqrt{3} T h e r e f o r e, a = 11, b = - 6 F o r r e m a i n i n g q u e r i e s w e r e q u e s t y o u t o p o s t t h e m i n s e p a r a t e t h r e a d s t o h a v e r a p i d a s s i s \tan c e f r o m o u r e x p e r t s . R e g a r d s

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