IT took me a while to learn how to flip flapjacks. In fact, a+1/a=6, then the value of a^2 + 1/a^2 is the number of attempts it took me. How many attempts did it take me?

A. 34
B. 35
C. 36
D. 38

I don't know how to do it, I'm assuming that 1 1/a =6, but I'm wrong I think. help!

first of all, for a + 1/a to be equal to 6, a would not be a "nice" number

we could find it ....
a + 1/a = 6
multiply each term by a
a^2 + 1 = 6a
a^2 - 6a + 1 = 0
a = (6 ± √32)/2 = 3 ± 2√2 , not nice as predicted
we could square that, and then take the reciprocal and simplify, but that looks rather messy

other way:

note that (a + 1/a)^2 ≠ a^2 + 1/a^2
but we want a^2 + 1/a^2

let's see what it is ...

(a + 1/a)^2 = a^2 + 2(a)(1/a) + 1/a^2
ahhh...
6^2 = a^2 + 2 + 2(6)
36 - 2 = a^2 + 1/a^2

a^2 + 1/a^2 = 34

you can verify this by evaluating a on your calculator and
doing it, it is correct