1.

For a inR, if |x - a + 3| + |x-3a|=2x - 4a +3 | is ture AA x inR.Then find the value of a.

Answer»

Solution :`|x - a + 3| + |x-3a|=2x - 4a +3|`
`rArr|x - a + 3| + |x-3a|=|(x - a +3) + (x - 3a)|`
`rArr(x - a + 3 )(x - 3a)ge0 AA x in`R.
`rArrx^(2) + x (3 - 4a) + 3a (a - 3) ge 0, AA x in N` R.
For the above inequality,
`D LE 0`
`rArr(3 - 4 a)^(2) - 12 a (a - 3) le 0`
`rArr(2a + 3)^(2) le 0`
`rArra = - 3//2`


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