pankajks2010 wrote:Hi,
This question is from Manhattan flash cards.
Find the value of x: (x+3)^(1/2) = x-3
The OA is only 6 and not 1. will be great, if someone could help why 1 is not a possible answer.
I received a PM asking me to comment.
The MGMAT flash card reads as follows:
√(x+3) = x-3
The √ symbol means "positive root only".
Thus, if we solve by squaring both sides, we can consider only the positive root of √(x+3):
(√(x+3))² = (x-3)²
x+3 = x² - 6x + 9
x² - 7x + 6 = 0
(x-6)(x-1) = 0
x = 6, 1.
But x=1 results in the negative square root of √(x+3) and thus is not allowed:
√(1+3) = 1-3
√4 = -2.
Since √ means the positive root only, only x=6 is possible:
√(6+3) = 6-3
√9 = 3.
Thus, the only possible solution is x=6.
So remember what the different notations imply:
√16 = 4.
However, if x²=16, then x = ±4.
This is an important distinction to remember when taking the GMAT.
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