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The equation ||x-2|+a|=4 can have four d...

The equation `||x-2|+a|=4` can have four distinct real solutions for `x` if `a` belongs to the interval `(-oo,-4)` (b) `(-oo,0)` `(4,oo)` (d) none of these

A

`(-oo,4)`

B

`(-oo,-4)`

C

`(4,oo)`

D

`[-4,4]`

Text Solution

Verified by Experts

The correct Answer is:
B
`||x-1|+a|=4`
`implies|x-1|+a=+-4`
`implies|x-1|=+-a`
For real solutions, we must have
`+-4-a gt 0`
`implies 4-a ge0` and `-4-a ge0`
`ale4` and `a le-4`
`implies ale-4 implies ale4 implies a in(-oo,-4]`
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OBJECTIVE RD SHARMA ENGLISH-MISCELLANEOUS EQUATIONS AND INEQUATIONS -Chapter Test
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