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`1,`
`(x-1)(x-2)+5`
`= x^2 - 2x - x+2+5`
`= x^2 - 3x + 7`
`= x^2 - 2 . x . 3/2 + (3/2)^2 +19/4`
`= (x-3/2)^2 + 19/4 ≥ 19/4 > 0∀x`
`-> (x-1)(x-2)+5 >0 ∀x`
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`2,`
`4x - x^2 - 5`
`= -x^2 +4x-5`
`= - (x^2 - 4x +5)`
`=- (x^2 - 2 . x . 2 + 2^2 +1)`
`= - (x-2)^2 - 1 ≤ -1 < 0∀x`
`-> 4x-x^2 - 5 < 0∀x`
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`3,`
`(1-2x)(x-1)-5`
`= x - 1 - 2x^2 + 2x-5`
`= -2x^2 + 3x - 6`
`= -2 (x^2 - 3/2x + 3)`
`= - 2 (x^2 - 2 . x . 3/4 + 9/16 + 39/16)`
`= -2 (x - 3/4)^2 - 39/8 ≤ (-39)/8 < 0∀x`
`-> (1-2x)(x-1)-5 < 0∀x`
