if x€R then find minimum value of |x-1|2x-1|.... |119x-1|
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if x€R then find minimum value of |x-1|2x-1|.... |119x-1|
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Answer:
x−1∣+∣2x−1∣+∣3x−1∣+......+∣119x−1∣
=x−1+2x−1+3x−1+....+119x−1
=x(1+2+3....+119)−119
=x(
2
119×120
)−119
=119(60x−1) .
Minimum value= 0 occurs when 60x−1=0
⇒60x=1
⇒x=1/60 .
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