Question

pls answer it fast and with explanation ​

Answer 1

Answer:

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Answer 2

Answer:

${a}^{2} - {b}^{2} = \frac{795 - 240 \sqrt{11} }{20 - 6 \sqrt{11} }$

Step-by-step explanation:

$a = \frac{1}{3 - \sqrt{11} }, \: b= \frac{1}{a} = \frac{1}{ \frac{1}{3- \sqrt{11} } } = 3- \sqrt{11} \\ {a}^{2} - {b}^{2} \\ = {( \frac{1}{3 - \sqrt{11} }) }^{2} - { (3 - \sqrt{11} )}^{2} \\ = \frac{1}{9 + 11 - 6 \sqrt{11} } - (9 + 11 - 6 \sqrt{11} ) \\ = \frac{1}{20 - 6 \sqrt{11} } - (20 - 6 \sqrt{11} ) \\ = \frac{1 - {(20 - 6 \sqrt{11}) }^{2} }{20 - 6 \sqrt{11} } \\ = \frac{1 - (400 + 396 - 240 \sqrt{11}) }{20 - 6 \sqrt{11} } \\ = \frac{1 - 400 - 396 + 240 \sqrt{11} }{20 - 6 \sqrt{11} } \\ = \frac{( - 795) + 240 \sqrt{11} }{20 - 6 \sqrt{11} } \\ = \frac{795 - 240 \sqrt{11} }{20 - 6 \sqrt{11} }$