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CBSE Class 11-science Answered

I can't understand why they have taken y is element of [1/3,3],as above image shows that they don't have the specified part common. 
Asked by Vineeth K | 12 Apr, 2016, 06:03: PM
answered-by-expert Expert Answer
Given space equation space is space open parentheses straight y space minus space 1 third close parentheses open parentheses straight y minus 3 close parentheses less or equal than 0.
Product space of space two space terms space will space be space less space than space zero space if space one space of space the space term space is space negative space and space another space term space is space positive.

So space there space will space be space two space cases.
straight y space less or equal than 1 third
rightwards double arrow straight y element of left parenthesis negative infinity comma 1 third right square bracket

straight y space less or equal than 3
rightwards double arrow straight y element of left parenthesis negative infinity comma 3 right square bracket

If space we space take space common space part space space then space it space will space be space left parenthesis negative infinity comma 1 third right square bracket.
If space we space take space straight y element of left parenthesis negative infinity comma 1 third right square bracket
So space the space value space of space space open parentheses straight y space minus space 1 third close parentheses open parentheses straight y minus 3 close parentheses space space greater or equal than 0 space space Which space is space not space what space we space wanted.


So space we space will space have space to space take space the space interval space such space that space one space term space is space will space be space positive space and space another space term space is space negative.
If space we space take space open square brackets 1 third comma 3 close square brackets
then space open parentheses straight y space minus space 1 third close parentheses greater or equal than 0 space and space open parentheses straight y minus 3 close parentheses less or equal than 0 space and space the space product space is space space open parentheses straight y space minus space 1 third close parentheses open parentheses straight y minus 3 close parentheses less or equal than 0.
Answered by Vijaykumar Wani | 13 Apr, 2016, 04:54: PM
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