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`(sqrt(8+2x-x^2)>6-3x)`

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Verified by Experts

The correct Answer is:
`x in (1,4]`
`sqrt(8+2x-x^(2)) gt 6-3x`
We must `8+2x-x^(2) ge 0`
`implies x in [-2,4 ]` …….`(i)`
For `6-2x lt 0` or `x gt 2` , inequality is satisfied.
Let `6-3x ge 0`
`implies x le 2`…….`(ii)`
`implies 8+2x-x^(2) gt 36+9x^(2)-36x`
`implies 5x^(2)-19x+14 lt 0`
`implies (5x-14)(x-1) lt 0`
`implies x in (1,(14)/(5))`.........`(iii)`
From `(ii)` and `(iii)`, `x in (1,2]`
`:. "finally" x in (1,4]`
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CENGAGE-INEQUALITIES AND MODULUS-Single correct Answer
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