7The Q reduces to (84+n)/10.
given, y = |x| + |x - 1| + |x - 3| + |x - 6| + .................. + |x - 5151|
let m = no. of terms in the expression y
and, n = no. of integers for which y has min. value
then find the value of
m + n - 1810
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4 Answers
1708\hspace{-16}$Here $\bf{y=\mid x \mid+\mid x-1\mid+\mid x-3 \mid+\mid x-6 \mid+........+\mid x-5151\mid}$\\\\\\ So Total no. of terms in $\bf{y}$ is equal to $\bf{m=102}$\\\\\\ Using Total no. of terms in $\bf{\mid x-1\mid+\mid x-3 \mid+\mid x-6 \mid+........+\mid x-5151\mid}$\\\\\\ is $\bf{=101}$ and one term is $\bf{\mid x \mid}$\\\\\\ So Total $\bf{m=101+1=102}$\\\\\\ Now Min.$\bf{y=\mid x \mid+\mid x-1\mid+\mid x-3 \mid+\mid x-6 \mid+........+\mid x-5151\mid}$\\\\\\ Min. occur at $\bf{51^{th}}$ to $\bf{52^{th}}$ term\\\\\\ Which is $\bf{x=1275}$ to $\bf{x=1326}$\\\\\\ So Here $\bf{y_{Min.}}$ at $\bf{1275\leq x\leq 1326\;\;,x\in \mathbb{Z^{+}}}$\\\\\\ So Total value of $\bf{x}$ is $\bf{n=52}$\\\\\\ So $\bf{\frac{m+n-18}{10}=\frac{102+52-18}{10}=\frac{136}{2}=13.6}$
36@man111 - wonderful...!!
actually the expression was m + n - 1018 which gives 8...!!