+128475 Abs (a - b) will be largest when at least one of the other terms is minimized....so, since absolute value is always ≥ 0, let's minimize the middle term by letting b = c
This gives us
abs ( a - b) + abs(c - a) = 20 but, since b= c, we can write
abs ( a - b) + abs(b - a) = 20 and let's assume that a > b [we could also assume the opposite....it won't matter]
So we have, using the definition of absolute value:
a - b + -(b - a) = 20
a - b + a - b = 20
2(a - b) = 20
(a - b) = 10
Which implies that
abs (a - b) = 10
And that's as large as abs(a - b) can be
--------------------------------------------------------------------------------------------------------------------------
As Melody would say.......that's what I think..!!!.....of course....any constructive criticism is welcome....!!!
+128475 Abs (a - b) will be largest when at least one of the other terms is minimized....so, since absolute value is always ≥ 0, let's minimize the middle term by letting b = c
This gives us
abs ( a - b) + abs(c - a) = 20 but, since b= c, we can write
abs ( a - b) + abs(b - a) = 20 and let's assume that a > b [we could also assume the opposite....it won't matter]
So we have, using the definition of absolute value:
a - b + -(b - a) = 20
a - b + a - b = 20
2(a - b) = 20
(a - b) = 10
Which implies that
abs (a - b) = 10
And that's as large as abs(a - b) can be
--------------------------------------------------------------------------------------------------------------------------
As Melody would say.......that's what I think..!!!.....of course....any constructive criticism is welcome....!!!
