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CBSE Class 11-science Answered

If we know two inequalities for a number k, how should we combine them?

Like ( k is greater than 2) and ( {k+6}{k-4} is greater than 0).

What will be k ultimately?

Asked by drhimasingh | 23 Apr, 2020, 11:34: AM
Expert Answer
The inequalities are given as follows:
k>2 ... (i) and (k+6)(k-4)>0 ... (ii)
The second inquality holds true when the factor are either both positive or both negative.
i.e. (k+6)>0 and (K-4)>0    or    (k+6)<0 and (k-4)<0
In the first case, k>-6 and k>4 which implies k>4
In the second case, k<-6 and k<4 which implies k<-6
From both the cases, we have k>4 or k<-6
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B u t space f r o m space t h e space f i r s t space i n e q u a l i t y comma space w e space h a v e space k greater than 2 space rightwards double arrow k element of open parentheses 2 comma space infinity close parentheses
I n t e r s e c t i o n space o f space open parentheses 2 comma space infinity close parentheses space a n d space open parentheses negative infinity comma negative 6 close parentheses union open parentheses 4 comma space infinity close parentheses space i s space open parentheses 4 comma space infinity close parentheses
H e n c e comma space k element of open parentheses 4 comma space infinity close parentheses space i. e. space k greater than 4
Answered by Renu Varma | 23 Apr, 2020, 12:30: PM
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