Processing Math: Done

From Förberedande kurs i matematik 1

Using the rule (a+b)2=a2+2ab+b2, we recognize the polynomial as the expansion of (x−1)2,

x2−2x+1=(x−1)2.

This quadratic expression has its smallest value, zero, when x−1=0, i.e. x=1. All non-zero values of x−1 give a positive value for (x−1)2.

Note: If we draw the curve y=(x−1)2, we see that it has a minimum value of zero at x=1.