 # Understand the problem

Suppose that the number $a$ satisfies the equation $a$+$\frac{1}{a}$=$4$ What is the value of $a^4$+$\frac{1}{a^4}$?

(a) 164.        (b)172.       (c)192.       (d)194.       (e)212

##### Source of the problem

American Mathematical Contest 2007 10 A Problem 20

Basic Algebra

4/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

Step 1. Look’s hard , lets see we are given with $a$+$\frac{1}{a}$=$4$ and we need to find $a^4$+$\frac{1}{a^4}$. So first we will square both sides in order to get  $a^2$+$\frac{1}{a^2}$ and find its value. Give it a try!!!!.
Step 2. We reached the power 2 now aim is to get to power 4. Now After getting the the value of  $a^2$+$\frac{1}{a^2}$ , again square both sides to get the value of the expression $a^4$+$\frac{1}{a^4}$ . Very close to the solution !!!!!!.
Step 3 . Now we get the equation $a^4$+$\frac{1}{a^4}$ after solving  $(a^2+\frac{1}{a^2})^2$. Now I hope u can see the answer by your self just a last step!!!!.
Step 4 By solving we get the results that is   $a^2$+$\frac{1}{a^2}$=14
and $a^4$+$\frac{1}{a^4}$ =194 which is our required value to find ,thats it!!!