Question

Please solve this problem in a different sheet!! Thank you in advance for your help!!

Answer 1

$Given: \frac{ \sqrt{7} - 1 }{ \sqrt{7} + 1 } - \frac{ \sqrt{7} + 1 }{ \sqrt{7} - 1}$

On cross multiplication, we get

$\frac{( \sqrt{7} - 1)^2 - ( \sqrt{7} + 1)^2 }{ (\sqrt{7} + 1)( \sqrt{7} - 1) } = a + b \sqrt{7}$

$\frac{(7 + 1 - 2 \sqrt{7}) - (7 + 1 + 2 \sqrt{7}) }{( \sqrt{7})^2 - (1)^2 }$ 

$\frac{8 - 2 \sqrt{7} - 8 - 2 \sqrt{7} }{7 - 1} = a + b \sqrt{7}$

$\frac{-4 \sqrt{7} }{6} = a + b \sqrt{7}$

$\frac{-2}{3} \sqrt{7} = a + b \sqrt{7}$

$0 + ( \frac{-2}{3}} ) \sqrt{7} = a +b \sqrt{7}$


Therefore:

$a = 0, b = \frac{-2}{3}$


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks