Question

Determine a and b if​

Answer 1

Answer:

000000000000000000000000

Answer 2

$\quad \ \ \frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow \frac{ {(7 + \sqrt{5}) }^{2} - {(7 - \sqrt{5}) }^{2} }{(7 - \sqrt{5} )(7 + \sqrt{5} )} = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow \frac{ (54 + 14 \sqrt{5} ) - (54 - 14 \sqrt{5} )}{ {(7)}^{2} - {( \sqrt{5} )}^{2} } = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow \frac{ \cancel{54} + 14 \sqrt{5} - \cancel{54}+ 14 \sqrt{5} }{49 - 5} = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow \frac{ {}^{7} \cancel{28} \sqrt{5} }{ \cancel{44} _{11} } = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow \frac{7 \sqrt{5} }{11} = {\footnotesize{ a + 7 \sqrt{5} b}}$

$\Rightarrow {\footnotesize{0 + 7 \sqrt{5} \:( \frac{1}{11} ) = a + 7 \sqrt{5} b}}$

On comparing,

• a = 0
• b = 1/11

....