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19 Mar 2019, 00:22
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:05) correct
43%
(01:39)
wrong
based on 268
sessions
History
Date
Time
Result
Not Attempted Yet
For which of the following values of k does the equation \(\frac{x-1}{x-2} = \frac{x-k}{x-6}\) have no solution for x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
19 Mar 2019, 00:58
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Solution
Given:
- • An equation: (x−1)/(x−2) = (x−k)/(x−6)
To find:
- • The value of k, for which the equation does have no solution.
Approach and Working:
Simplifying the equation, we get:
- • (x−1)/(x−2) = (x−k)/(x−6)
Or, (x – 1) (x – 6) = (x – 2) (x – k)
Or, x^2 – 7x + 6 = x^2 – x (2 + k) + 2k
Or, 7x – 6 = (2 + k) x – 2k
Or, x (7 – 2 – k) = 6 – 2k
Or, x = (6 – 2k)/(5 – k)
For no solution of this equation, 5 – k = 0, implies k = 5
Hence, the correct answer is option E.
Answer: E
General Discussion
25 Aug 2024, 13:04
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Rohan271
If k = 1, then we get \(\frac{x-1}{x-2} = \frac{x-1}{x-6}\), which has a solution x = 1. You see we cannot reduce by x - 1 because we loos a root, specifically x - 1 = 0, which gives x = 1.
