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If a,b in R distinct numbers satisfying ...

If a,b `in` R distinct numbers satisfying |a-1| + |b-1| = |a| + |b| = |a+1| + |b+1|, Then the minimum value of |a-b| is :

A

a) 3

B

b) 0

C

c) 1

D

d) 2

Text Solution

Verified by Experts

The correct Answer is:
D
Let `altb and f(x)=|x-a|+|x-b| AA x in R`
So, f(x) decreasing in `(-oo,a)` constant in [a, b] and increasing in `[b,oo]`
`|a-1|+|b-1|=|a|+|b|=|a+1|+|b+1|`
`rArr" "f(0)=f(1)=f(-1)`
`rArr" "{-1,0,1} in {a,b}`
`therefore" "|a-b|_("min")=2.`
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