Answer:
See below for solution.
Step-by-step explanation:
[tex]Q13)[/tex] [tex]\frac{\sqrt{11} - \sqrt{5} }{\sqrt{11}+\sqrt{5} }[/tex] = [tex]x - y\sqrt{55}[/tex]
LHS :-
= [tex]\frac{\sqrt{11} - \sqrt{5} (\sqrt{11}-\sqrt{5}) }{\sqrt{11}+\sqrt{5} (\sqrt{11}-\sqrt{5}) }[/tex]
= [tex]\frac{11-2\sqrt{55}+5 }{11 - 5}[/tex]
= [tex]\frac{16-2\sqrt{55} }{6}[/tex]
= [tex]\frac{2(8-\sqrt{55}) }{2(3)}[/tex]
= [tex]\frac{8-\sqrt{55} }{3}[/tex]
=> x = 8/3 and y = 1/3
=> Option B
[tex]Q14)[/tex] [tex]\frac{4}{216^{-2/3} }[/tex] + [tex]\frac{1}{256^{-3/4} }[/tex] + [tex]\frac{2}{243^{-1/5} }[/tex]
= 4 x (∛216)² + ([tex]\sqrt[4]256}[/tex])³ + 2 x ([tex]\sqrt[5]{243}[/tex])
= 4 x 36 + 64 + 2 x 3
= 144 + 64 +6
= 144 + 70
= 214
