Hi,

This is MGMAT Guide #2, 6th edition, Algebra, regarding Question 7 of the Chapter 12 problem set (page 179). (Please note I'm using "^(1/2)" instead of the root sign in reproducing this question - can't figure out how to type a root sign!)

"If g(x) = 3x + x^(1/2), what is the value of g(d^2 + 6d + 9)?"

The solution on page 182 says "3d^2 + 19d + 30 OR 3d^2 + 17d + 24."

I understand how to arrive at the first solution, but the explanation for the second solution reads:

g(d^2 + 6d + 9) = 3(d^2 + 6d + 9) + (d^2 + 6d + 9)^(1/2)

= 3d^2 + 18d + 27 + ((d+3)^2)^(1/2)

= 3d^2 + 18d + 27 - (d+3)

= 3d^2 + 17d + 24

However, back on page 71, we covered that "If a given equation contains a square root symbol on the GMAT, only use the positive root." This second possible solution above seems to use the negative root of ((d+3)^2)^(1/2). (Again, noting that the problem uses a square root symbol, not the "raised to the one-half" way I'm noting it here. What am I missing here? Shouldn't we have only considered the positive root?

Thanks in advance!