<p>The set of all real numbers x such that sqrt((x)^2) = -x consists of </p>
<p>a zero only
b non positive real numbers only
c positive real numbers only
d all real numbers
e no real numbers </p>
<p>answer is B</p>
<p>The explanation in the book was confusing, thanks</p>
<p>Do casework based on whether x is positive, negative, or zero.</p>
<p>The square root of a squared number is always the original number. So sqrt((a)^2) = a. </p>
<p>This is saying that you need to find the set of values so that when you square those, then take the square root of it, you’ll end up with a negative number. The answer is therefore negative real numbers. If x = -9, you square it, you’ll get 81. You the the square root, which can be positive or negative, and you get + or - 9.</p>
<p>Actually, it goes something like this:
The sqrt function (shown in longhand writing as a square root sign with a hook at the end) returns only the positive value (like on a calculator). Interestingly, this is why the formula for solving quadratic equations includes the phrase “…plus or minus the square root of…” </p>
<p>So continuing with the -9 example, the square of -9 is 81. But sqrt(81) returns +9. Happy news: +9 is the same as -(-9), or -x as specified in the question. It extends to all real negative numbers.</p>
<p>On the other hand, if you were to work the same thing with +9, and the same sqrt() value of +9, you find that +9 is not equal to -(+9); in other words, sqrt((x)^2) is not equal to -x. Hence all real positive numbers are knocked out of the set.</p>
<p>As for zero, it just plays out as zero all through, so it’s included in the set too. That’s why the complete answer is non-positive real numbers.</p>
<p>Hope this was helpful :)</p>
<p>even though i didn’t post the question, thanks a lot. i wasn’t thinking about it the correct way.</p>
<p>"The square root of a squared number is always the original number. So sqrt((a)^2) = a. "</p>
<p>Not quite. It turns out that sqrt(x^2) = |x|. The OP’s question is basically solving |x| = -x, which occurs when x is not positive.</p>