If the expression (mx-1+1/x) is always non negative then the minimum  value of 'm' must be

Asked by dev.sultanpur123 | 5th Jun, 2015, 07:18: PM

Expert Answer:

m x minus 1 plus 1 over x greater or equal than 0 rightwards double arrow fraction numerator m x squared minus x plus 1 over denominator x end fraction greater or equal than 0 S o space e i t h e r space b o t h space n u m e r a t o r space a n d space t h e space d e n o m i n a t o r space a r e space greater or equal than 0 space comma space left parenthesis x not equal to 0 right parenthesis space o r space b o t h space n u m e r a t o r space a n d space t h e space d e n o m i n a t o r space a r e space less or equal than 0 space comma space left parenthesis x not equal to 0 right parenthesis m x squared minus x plus 1 greater or equal than 0 space a l w a y s space o r space m x squared minus x plus 1 space less or equal than 0 space a l w a y s. space m x squared minus x plus 1 greater or equal than 0 space a l w a y s space i s space p o s s i b l e space i f space m greater than 0 space a n d space D less or equal than 0 rightwards double arrow m greater than 0 space a n d space 1 minus 4 m less or equal than 0 rightwards double arrow m greater than 0 space a n d space m greater or equal than 1 fourth rightwards double arrow m greater or equal than 1 fourth.... left parenthesis 1 right parenthesis m x squared minus x plus 1 less or equal than 0 space a l w a y s space i s space p o s s i b l e space i f space m less than 0 space a n d space D less or equal than 0 rightwards double arrow m less than 0 space a n d space 1 minus 4 m less or equal than 0 rightwards double arrow m less than 0 space a n d space m greater or equal than 1 fourth N o t space p o s s i b l e space s i m u l tan e o u s l y. H e n c e comma space f r o m space left parenthesis 1 right parenthesis space w e space g e t space m i n i m u m space p o s s i b l e space v a l u e space o f space m space i s space 1 fourth.

Answered by satyajit samal | 6th Jun, 2015, 09:21: PM

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