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it is a common mistake to assume sqrt(x^2) is x. it could be -x if x <0.
for example in this case sqrt(y-1)^2 would not be y-1, it would be 1-y (since y-1 is -ve)
in simple words, sqrt((-3/5)^2) = 3/5, not -3/5
Jeez! scary.
y ^ 2 - 2y + 1 can be written as (y-1) ^ 2 or (1-y) ^2.
But why do we have to chose (1-y) over (y-1). I felt like I understood and then I lost the train of thought.
1-y = 3/5 and y-1 = -3/5. In either case the value of square is same.
We should not take the sqrt away before and call it (y-1). The calculation must be done inside the sqrt and then removed.
if y - 1 is negative and if you do the calculation and then deduce the square root, you would come up with 1 - y. The point is that there's a small trick here to avoid those calculations: if y - 1 is positive, forget calculations and cancel square with square root. if it is negative, cancel and negate the expression.
This is the place where non-real number is being tested. If I write sqrt(-4) * sqrt(-4), I am multiplying two imaginary numbers.
I had posted my query on the site asking whether anyone has experienced imaginary number related questions in GMAT and I got answer in negation. I think, this question helps me get the answer.
This is the place where non-real number is being tested. If I write sqrt(-4) * sqrt(-4), I am multiplying two imaginary numbers.
I had posted my query on the site asking whether anyone has experienced imaginary number related questions in GMAT and I got answer in negation. I think, this question helps me get the answer.