Lösung 2.3:6a
Aus Online Mathematik Brückenkurs 1
Using the squaring rule, we recognize the polynomial as the expansion of \displaystyle \left( x-1 \right)^{2},
\displaystyle x^{2}-2x+1=\left( x-1 \right)^{2}
This quadratic expression has its smallest value, zero, when
\displaystyle x-\text{1}=0, i.e.
\displaystyle x=\text{1}. All non-zero values of
\displaystyle x-\text{1}
give a positive value for
\displaystyle \left( x-1 \right)^{2}.
NOTE: If we draw the curve \displaystyle y=\left( x-1 \right)^{2}, we see that it has a minimum value of zero at \displaystyle x=\text{1}.
