a) \(A=x^2-2x+2=\left(x-1\right)^2+1>0\forall x\inℝ\)
b) \(x-x^2-3=-\left(x^2-x+3\right)\)
\(=-\left(x^2-x+\frac{1}{4}+\frac{11}{4}\right)\)
\(=-\left[\left(x-\frac{1}{2}\right)^2+\frac{11}{4}\right]\)
\(=-\left[\left(x-\frac{1}{2}\right)^2\right]-\frac{11}{4}\le\frac{-11}{4}< 0\forall x\inℝ\)
x²-2x+2=(x²-2x+1)+1=( x-1)²+1
Mà (x-1)²≥0 với mọi x
=> (x-1)²+1>0 với mọi x
=> x²-2x+2>0 với mọi x