Hi All,
This question is built around the concept of reciprocals. While some Test Takers might be able to spot the logic involved, most would probably need to TEST VALUES so that they can 'see' what the rule/pattern is:
We're told that X > 0. We're asked for the LEAST possible value of X + 1/X.
To start, X and 1/X are reciprocals, meaning that when you plug in a value for X, you'll get the inverse of that value for 1/X.
For example...
X = 10
1/X = 1/10
Sum = 10.1
X = 1/2
1/X = 1/(1/2) = 2
Sum = 2.5
From these two example, we can see that the sum of the two terms WILL be greater than 1. It's just a matter of how 'close to 1' we can get the sum...
When...
X = 1
1/X = 1
So the sum is 1+1 = 2
There's no other example that will get us any lower than 2, so that must be the answer.
Final Answer:
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Rich
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