gmattesttaker2 wrote:
If 4^x + 4^(-x) = 2, what is the value of x?
A) -1
B) -1/2
C) 0
D) 1/2
E) 1
As you can see, solving this question algebraically can take a lot of time.
Mitch pointed out that checking the answer choices is the best route, and I thought I'd quickly mention that we can quickly eliminate some of the answer choices.
Notice that,
if b^k is an integer, then b^(-k) will not be an integer, and vice versa. The only time when this is not true is when k=0, or when b = 0, 1 or -1. Since the base (b) equals 4 in this question, the second part of that proviso doesn't count here.
So, for example, when we examine answer choice A (x=-1), we can see that 4^(-x) = 4^1 = 4. Since 4^(-x) is an integer, we immediately know that 4^x is
not an integer. Since there's no way that an integer plus a non-integer can equal 2, we can eliminate A.
Likewise, without performing any calculations, we can eliminate E.
The same applies to answer choices B and D,
HOWEVER, if we're checking answer choices, we should be checking the easiest options first. So, once we eliminate 1 and -1 (answers A and E), we should probably check C (x=0) before we start checking fractions.
Cheers,
Brent
