From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	Using the rule <math>(a+b)^2=a^2+2ab+b^2</math>, we recognize the polynomial as the expansion of <math>(x-1)^{2}\,</math>,
-	<center> [[Bild:2_3_6a.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}
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		+	This quadratic expression has its smallest value, zero, when <math>x-1=0</math>, i.e.
		+	<math>x=1</math>. All non-zero values of <math>x-1</math> give a positive value for
		+	<math>(x-1)^{2}</math>.
		+
		+
		+	Note: If we draw the curve <math>y=(x-1)^{2}</math>, we see that it has a minimum value of zero at <math>x=1\,</math>.
		+
		+
		+	[[Image:2_3_6_a.gif|center]]

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Current revision

Using the rule \displaystyle (a+b)^2=a^2+2ab+b^2, we recognize the polynomial as the expansion of \displaystyle (x-1)^{2}\,,

\displaystyle x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}

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

Note: If we draw the curve \displaystyle y=(x-1)^{2}, we see that it has a minimum value of zero at \displaystyle x=1\,.