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
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