Question

If a+1/a=5

, find the value of a^4+1/a^4

Answer 1

`(a+1)/(a)=5\\\\(a)/(a)+(1)/(a)=5\\\\1+(1)/(a)=5\qquad\text{subtract 1 from both sides}\\\\(1)/(a)=4\\\\\left((1)/(a)\right)^4=4^4\\\\(1)/(a^4)=256\qquad(*)\\-----------------------\\\\(a^4+1)/(a^4)=(a^4)/(a^4)+(1)/(a^4)=1+\underbrace{(1)/(a^4)}_((*))=1+256=257`