Explanation

In this question, we are given an expression that includes two variables, and . We are going to have to get some more information and use exponent rules to try to confirm whether this would-be equation with the question mark is true. On to the statements, separately first.

Statement (1) looks like it may be the square root of what we looking for, especially because the right side of it, , is the square root of the variable . So, let's square this expression and proceed by the rules. The best way to proceed carefully when you are doing something to a side of an equation, such as squaring or multiplying by 1, is to encapsulate that side of the equation in parentheses in then apply the operator, like so:



This notation will prevent the error of squaring each of the terms on the left individually and thinking that doing so amounts to squaring the entire left side, which it doesn't. To square the left side, we will have to use FOIL. Each of the elements will get multiplied by the other once and added.













We now have a statement that we can compare directly with the question posed. The statement we have obtained is almost the same, but greater by 2. The question asks us, "Is equal to this expression?" Statement (1) gives a definitive answer: "Actually, no, it's equal to this other expression, which is similar but unequal." We have sufficient information to answer the question definitively in the negative, so Statement (1) is sufficient.

Statement (2) allows for a whole possible range of values of , and it doesn't say anything about , so it doesn't provide enough information to prove the statement correct or incorrect. Insufficient.

Before we go, we might double-check that Statement (1) was sufficient without the knowledge that a is positive, since Statement (2) looks suggestive. But, indeed, in the case of Statement (1) we used rules and not any knowledge about whether a is positive or negative in order to arrive at our result. You can also see, on examining the prompt, that it wouldn't matter whether a is positive or negative--it would just switch the terms on the left, in a manner of speaking.

The correct answer is (A).