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question mark

find minimum value of

mod(2z-1) + mod(3z-2)

Nilesh Joshi , 14 Years ago
Grade
anser 3 Answers
SAGAR SINGH - IIT DELHI

Last Activity: 14 Years ago

Dear student,
mod(2z-1)=mod(2x-1+i2y)<root(4x2+-4x+4y2)
mod(3z-2)=mod(3x-2+i3y)< root(9x2+4-12x+9y2)
nowfind the minimum value easily....
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Sagar Singh
B.Tech, IIT Delhi

sdf

Last Activity: 8 Years ago

please give answer

mycroft holmes

Last Activity: 8 Years ago

2|z-1/2|+3|z-2/3| = 2[ |z-1/2|+|2/3 – z| ] + |z-2/3]
By triangle inequality we have that the expression
\ge 2 \left|\frac{2}{3} - \frac{1}{2} \right| + \left|z -\frac{2}{3} \right|
\ge \frac{1}{3} + \left|z -\frac{2}{3} \right|
Equality occurs when z = 2/3
Hence min is 2/3

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