Question

please solve this question​

Answer 1

First, notice that (a + 1/a)2 = 42 = 16.  But also, (a + 1/a)2 = a2 + 2a(1/a) + 1/a2 = a2 + 2 + 1/a2 = a2 +  1/a2 + 2

 

So a2 + 1/a2 + 2 = 16, so a2 + 1/a2 = 14.

 

Now, do that again...

 

(a2 + 1/a2)2 = 142 = 196, but also (a2 + 1/a2)2 = a4 + 2(a2)(1/a2) + 1/a4 = a4 + 2 + 1/a4 = a4 + 1/a4 + 2

 

So a4 + 1/a4 + 2 = 196, so a4 + 1/a4 = 194