Question

Answer 1

1) \(x^2-2x+2=\left(x^2-2x+1\right)+1=\left(x-1\right)^2+1\ge0>0\forall x\)

2) \(6x-x^2-10=-\left(x^2-6x+9\right)-1=-\left(x-3\right)^2-1\le-1< 0\forall x\)

Answer 2

1: \(x^2-2x+2=\left(x-1\right)^2+1>0\forall x\)

2: \(6x-x^2-10\)

\(=-\left(x^2-6x+10\right)\)

\(=-\left(x-3\right)^2-1< 0\forall x\)

Answer 3