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Question

Question 4
If a=3+52, then find the value of a2+1a2.


Solution

Given, a=3+52
Now, 1a=23+5=23+5×3535
[Multiplying numerator and denominator by 35]
=62532(5)2 [Using identity, (ab)(a+b)=a2b2]
=62595=6254
1a=2(35)4=352
a2+1a2=a2+1a2+22=(a+1a)22             [adding and subtracting 2]
=(3+52+352)22          
=(62)22=(3)22=92=7

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