InterviewSolution
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InterviewSolution
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Solve the equatioin `|x-|4-x||-2x=4` |
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Answer» The equation is equivalent to the collection of systems `{(|x-(4-x)|-2x=4, "if"4-xge0),(|x+(4-x)|-2x=4, "if"4-xlt0):}` `implies {(|2x-4|-2x=4, "if"xle4),(4-2x=4,"if"xgt4):}`……I The second system of this collection gives `x=0` but `xgt4` Hence, second system has no solution. The first system of collection Eq. (i) is equivalent to the system of collection `{(2x-4-2x=4, "if"2xge4),(-2x+4-2x=4,"if"2xlt4):}` `implies{(-4=4,"if"xge2),(-4x=0,"if"xlt2):}` The first system is failed and second system gives `x=0`. Hence `x=0` is unique solution of the give equation. |
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