# Understand the problem

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

##### Source of the problem

American Mathematical Contest 2007 10 A Problem 20

##### Topic

Basic Algebra

##### Difficulty Level

4/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

# Start with hints

**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!!!