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If the equation x^(2)-4x-(3k-1)|x-2|-2k+...

If the equation `x^(2)-4x-(3k-1)|x-2|-2k+8=0,kinR`, has exactly three distinct solutions, then `k` is equal to _____.

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Verified by Experts

The correct Answer is:
2
Given equation is
`(x-2)^(2)-4-(3k-1)|x-2|-2k+8=0` or
`r^(2)-(3k-1)t-2k+4=0`, where `t=|x-2|`
For exactly 3 distinct solutions, one of the roots is zero and other root is positive.
`:.k=2`
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