Problem Solving

Hmna wrote:If x = 2 - √3 then the value of x^2 - x^(-2) will be ?

A) 14
B) -8√3
C) 7-4√3
D) 7+4√3

We can solve this question quickly if we ESTIMATE.
For the GMAT, it's useful to remember the following approximations:

√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, if x = 2 - √3, then we can write: x ≈ 2 - 1.7 ≈ 0.3

Now take x^2 - x^(-2) and replace x with 0.3
We get: x^2 - x^(-2) ≈ 0.3^2 - 0.3^(-2)
≈ 0.09 - 1/0.09
Since 0.09 is very close to 0.1, we can replace 0.09 to 0.1 to get...
≈ 0.1 - 1/0.1
≈ 0.1 - 10
≈ -9.9

Now check the answer choices...
A) 14 Not even close to -9.9, ELIMINATE
B) -8√3 ≈ (-8)(1.7). Looks promising. KEEP FOR NOW
C) 7-4√3 ≈ 7 - 4(1.7) ≈ 0. ELIMINATE
D) 7+4√3 ≈ 7 + 4(1.7). Not even close to -9.9, ELIMINATE

By the process of elimination, the correct answer is B


Cheers,
Brent