Which of the following always equals √ 9+x2−6x
x−3
3+x
|3−x|
|3+x|
3−x
OA c
Which of the following always equals √ 9+x2−6x
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By definition, √(x²) = |x|.guerrero wrote:Which of the following always equals √ 9+x2−6x
x−3
3+x
|3−x|
|3+x|
3−x
OA c
Thus:
√(9+x²-6x) = √(3-x)² = |3-x|.
The correct answer is C.
For some test-takers, an easier approach will be to plug in.
Note that -- by definition -- √ means the POSITIVE ROOT ONLY.
Since the correct answer choice must work for ALL values of x, be sure to try EXTREME values.
If x=1, then √(9+x²-6x) = √4 = 2.
Eliminate any answer choice that does not equal 2 when x=1:
x−3 = 1-3 = -2. Eliminate A.
3+x = 3+1 = 4. Eliminate B.
|3−x| = |3-1| = 2. Hold onto C.
|3+x| = |3+1| = 4. Eliminate D.
3−x = 3-1 = 2. Hold onto E.
If x=10, then √(9+x²-6x) = √49 = 7.
Eliminate any remaining answer choice that does not equal 7 when x=10:
|3−x| = |3-10| = 7. Hold onto C.
3−x = 3-10 = -7. Eliminate E.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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