- #1
anemone
Gold Member
MHB
POTW Director
- 3,883
- 115
Hey MHB, I am back, fully recover from food poisoning and first off, I want to take this opportunity to wish everyone and their family a very happy and Merry Christmas, much luck, good health and all good things of life. I hope you guys are able to spend it with loved ones!(Inlove)
I want to also present a "Christmas Math Challenge" as a gift to my friends (all of you are my friends, aren't you?:p) here today!
$a$ satisfies the equation $\left(a+\dfrac{1}{a}+1 \right)\left(a+\dfrac{1}{a} \right)=1$.
What is the value of $\left(a^{20}+\dfrac{1}{a^{20}}+1 \right)\left(a^{20}+\dfrac{1}{a^{20}} \right)$?
![1469966_10151725500306050_1957576524_n.jpg](https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash4/q71/s720x720/1469966_10151725500306050_1957576524_n.jpg)
I want to also present a "Christmas Math Challenge" as a gift to my friends (all of you are my friends, aren't you?:p) here today!
What is the value of $\left(a^{20}+\dfrac{1}{a^{20}}+1 \right)\left(a^{20}+\dfrac{1}{a^{20}} \right)$?