Question

if a and b are rational numbers and √11-√7/√11+√7=a-b√77,find the value of a and b

Answer 1

$\red{\mathcal{\huge{\underline{\star\:HEY\:MATE\:\star}}}}$

$<b>Solution:$

$\frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} } = a - b \sqrt{77} \\ \\ \frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} } \times \frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} - \sqrt{7} } \\ \\ \frac{( \sqrt{11} - \sqrt{7}) {}^{2} }{( \sqrt{11} ) {}^{2} - ( \sqrt{7}) {}^{2} } \\ \\ \frac{11 - 2 \sqrt{77} + 7 }{11 - 7} \\ \\ \frac{18 - 2 \sqrt{77} }{4} \\ \\ \frac{ \cancel2(9 - \sqrt{77} )}{ \cancel4 \: \: {}^{2} } \\ \\ \frac{9 - \sqrt{77} }{2}$

$\bold{\therefore{a = \frac{9}{2} \: and\:b= \frac {1}{2}}}$

$\red{\mathcal{\huge{\underline{\star\:Thanks\:\star}}}}$

Answer 2

_____________________________
♀ Your Solution ♀
_____________________________