Bunuel wrote:
If \(a + \frac{1}{a} = 4\) then what is the value of \(a^2 + \frac{1}{a^2}\) ?
A. 12
B. 14
C. 16
D. 18
E. 20
I really like the answer provided by
BrentGMATPrepNow.
Here's a second way to approach the problem if you aren't all that good at spotting the algebraic manipulation or tend to make errors in working with algebra.
\(a + \frac{1}{a} = 4\).
If we try 3 for a on the left side, we get 3.333. That's too small.
If we try 4 for a on the left side, we get 4.25. That's too big.
a has to be between 3 and 4.
If we try 3.5 for a on the left side, we get 3.5 + (1/3.5), which is less than 4. That's too small.
a has to be between 3.5 and 4.
Okay, now look at what we are asked to solve for.
\(a^2 + \frac{1}{a^2}\)
If we plug in 4, we get 16 + (1/16). Basically 16. But we need something smaller than that. Answer choices C, D, and E are wrong.
If we plug in 3.5, we get 12.25 + (1/12.25). But we need something larger than that. Answer choice A is wrong.
Answer choice B.
ThatDudeKnowsBallparking