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CBSE Class 11-science Answered

Find values of x for:- ||x-1|-2|=|x-3|
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Asked by 9377777388ts | 09 Aug, 2020, 05:36: PM
answered-by-expert Expert Answer
TO solve: ||x-1|-2|=|x-3|
If space straight x greater or equal than 1 rightwards double arrow straight x minus 1 greater or equal than 0 rightwards double arrow open vertical bar straight x minus 1 close vertical bar equals straight x minus 1 rightwards double arrow open vertical bar open vertical bar straight x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar straight x minus 1 minus 2 close vertical bar equals open vertical bar straight x minus 3 close vertical bar rightwards double arrow open vertical bar straight x minus 3 close vertical bar equals open vertical bar straight x minus 3 close vertical bar rightwards double arrow open vertical bar open vertical bar straight x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar straight x minus 3 close vertical bar space is space true space for space every space straight x greater or equal than 1 If space 0 less than straight x less than 1 space rightwards double arrow space straight x minus 1 less than 0 rightwards double arrow open vertical bar open vertical bar straight x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar negative straight x plus 1 minus 2 close vertical bar equals open vertical bar negative straight x minus 1 close vertical bar rightwards double arrow open vertical bar negative straight x minus 1 close vertical bar equals open vertical bar straight x minus 3 close vertical bar As space space 0 less than straight x rightwards double arrow negative straight x less than 0 rightwards double arrow negative straight x minus 1 less than negative 1 less than 0 rightwards double arrow open vertical bar negative straight x minus 1 close vertical bar equals negative left parenthesis negative straight x minus 1 right parenthesis equals straight x plus 1 rightwards double arrow straight x plus 1 equals negative left parenthesis straight x minus 3 right parenthesis space space... space since space straight x less than 1 less than 3 rightwards double arrow straight x plus 1 equals negative straight x plus 3 rightwards double arrow 2 straight x equals 2 rightwards double arrow straight x equals 1 Thus comma space open vertical bar open vertical bar straight x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar straight x minus 3 close vertical bar space is space true space for space every space straight x greater or equal than 1 Hence comma space the space solution space is space straight x element of left square bracket 1 comma space infinity right parenthesis.
Answered by Renu Varma | 13 Aug, 2020, 12:49: PM

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