a−1a=8
Squaring both sides,
=(a−1a)2=82
=a2+(1a)2−2(a)(1a)=64
=a2+1a2−2=64
=a2+1a2=66
Now,
(a+1a)2=a2+1a2+2(a)(1a)
=66+2
=68
=>a+1a=√68
=±2√17
a2−1a2=(a+1a)(a−1a)
=±(2√17)(8)
=±16√17
Prove that:(i) 13+√7+1√7+√5+1√5+√3+1√3+1=1(ii) 11+√2+1√2+√3+1√3+√4+1√4+√5+1√5+√6+1√6+√7+1√7+√8+1√8+√9=2