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Solution 2.3:6a

From Förberedande kurs i matematik 1

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m (Lösning 2.3:6a moved to Solution 2.3:6a: Robot: moved page)
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{{NAVCONTENT_START}}
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Using the squaring rule, we recognize the polynomial as the expansion of
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<center> [[Image:2_3_6a.gif]] </center>
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<math>\left( x-1 \right)^{2}</math>,
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{{NAVCONTENT_STOP}}
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<math>x^{2}-2x+1=\left( x-1 \right)^{2}</math>
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This quadratic expression has its smallest value, zero, when
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<math>x-\text{1}=0</math>, i.e.
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<math>x=\text{1}</math>. All non-zero values of
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<math>x-\text{1}</math>
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give a positive value for
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<math>\left( x-1 \right)^{2}</math>.
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NOTE: If we draw the curve
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<math>y=\left( x-1 \right)^{2}</math>, we see that it has a minimum value of zero at
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<math>x=\text{1}</math>.
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[[Image:2_3_6_a.gif|center]]
[[Image:2_3_6_a.gif|center]]

Revision as of 10:51, 21 September 2008

Using the squaring rule, we recognize the polynomial as the expansion of x12 ,


x22x+1=x12 


This quadratic expression has its smallest value, zero, when x1=0, i.e. x=1. All non-zero values of x1 give a positive value for x12 .

NOTE: If we draw the curve y=x12 , we see that it has a minimum value of zero at x=1.