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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:28) correct
42%
(01:45)
wrong
based on 191
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\sqrt{x - 1} - 7 = -x\), then x is equal to which of the following
I. 10
II. 5
III. 1
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
I. 10
II. 5
III. 1
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
02 Dec 2021, 07:49
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Bunuel
Don't waste any time solving the given equation. Here's why: Since this is an equation involving square root, once we perform all of the necessary steps and solve the equation for x, we must still check for extraneous roots by testing each value of x that we derived from our steps.
So, we can just skip the equation-solving part, and just test the three proposed values of x.
Here we go....
I. 10
Plug \(x = 10\) into the given equation to get: \(\sqrt{10 - 1} - 7 = -10\)
Simplify: \(\sqrt{9} - 7 = -10\)
Evaluate: \(3 - 7 = -10\) FALSE.
So, \(x = 10\) is NOT a solution
Important: Don't test anymore values. Since \(x = 10\) is NOT a solution, we can eliminate answer choices A, B, D and E, since they all suggest that \(x = 10\) IS a solution.
By the process of elimination, the correct answer must be C
OOPS! I just realized that answer choices A and B are the same.
Presumably, choice B should be II only.
So let's keep pressing values for the fun" of it....
II. 5
Plug \(x = 5\) into the given equation to get: \(\sqrt{5 - 1} - 7 = -5\)
Simplify: \(\sqrt{4} - 7 = -5\)
Evaluate: \(2 - 7 = -5\) WORKS.
So, \(x = 5\) IS a solution
III. 1
Plug \(x = 1\) into the given equation to get: \(\sqrt{1 - 1} - 7 = -1\)
Simplify: \(\sqrt{0} - 7 = -1\)
Evaluate: \(0 - 7 = -1\) FALSE.
So, \(x = 10\) is NOT a solution
So, ONLY II (x = 5) works.
