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If (x - 1)^(1/2) - 7 = -x, then x is equal then x is equal to
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29 Jan 2022, 06:32
29 Jan 2022, 06:32
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Question Stats:
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50% (01:49) wrong based on 4 sessions
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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
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Posts: 6218
Given Kudos: 136
If (x - 1)^(1/2) - 7 = -x, then x is equal then x is equal to
[#permalink]
29 Jan 2022, 06:41
29 Jan 2022, 06:41
1
Carcass wrote:
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
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
Since \(x = 10\) is NOT a solution, we can eliminate answer choices A, D and E, since they all suggest that \(x = 10\) IS a solution.
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
This means we can eliminate answer choice C, since it states that \(x = 5\) is NOT a solution
By the process of elimination, the correct answer is B.
gmatclubot
If (x - 1)^(1/2) - 7 = -x, then x is equal then x is equal to [#permalink]
29 Jan 2022, 06:41
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