The values of k for which the equation ∣∣|x−2|−5∣∣=k has 4 distinct solutions is
A
k∈[0,5]
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B
k∈[0,5)
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C
k∈(0,5)
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D
k∈(1,5]
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Solution
The correct option is Ck∈(0,5) |x−2|→ |x−2|−5→ ∣∣|x−2|−5∣∣→ Now for 4 distinct roots, the graph of y=k should intersect the above graph at 4 distinct point ⇒0<k<5 ∴k∈(0,5)