eitijan wrote:If x not equal to 0, then (√x²)/x =
A) -1
B) 0
C) 1
D) x
E) |x|/x
Case 1: x=2
In this case, (√x²)/x = (√2²)/2 = √4/2 = 2/2 = 1. This is our target.
Plugging x=2 into the answer choices, we get:
A) -1
B) 0
C) 1
D) x = 2
E) |x|/x = |1|/1 = 2/2 = 1
Only C and E yield our target value of 1.
Eliminate A, B and D.
Case 2: x=-2
In this case, (√x²)/x = (√(-2)²)/-2 = √4/-2 = 2/-2 = -1. This is our target.
Plugging x=-2 into the remaining answer choices, we get:
C) 1
E) |x|/x = |-2|/-2 = 2/-2 = -1
Only
E yields our target value of -1.
Eliminate C.
The correct answer is
E.
What is the flaw in below approach?
(x^2)^1/2=(x^2*1/2 )/x (by exponent rule) = x/x =1
The value in red is incorrect.
√(x²) ≠x.
By definition:
√ means the POSITIVE ROOT ONLY.
Thus:
√(x²) = the POSITIVE ROOT of x² = |x|.
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