Solution 2.3:1a

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m (Lösning 2.3:1a moved to Solution 2.3:1a: Robot: moved page)
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If we consider the squaring rule
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<center> [[Image:2_3_1a.gif]] </center>
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<math>\left( x-a \right)^{2}=x^{2}-2ax+a^{2}</math>
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and move
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<math>a^{2}</math>
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over to the left-hand side, we obtain the formula
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<math>\left( x-a \right)^{2}-a^{2}=x^{2}-2ax</math>
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<math></math>
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With the help of this formula, we can rewrite (complete the square of) a mixed expression
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<math>x^{2}-2ax</math>
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to a obtain a quadratic expression,
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<math>\left( x-a \right)^{2}-a^{2}</math>
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.
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The expression
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<math>x^{2}-2x</math>
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corresponds to
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<math>a=1</math>
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in the formula above and thus
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<math>x^{2}-2x=\left( x-1 \right)^{2}-1</math>

Revision as of 09:53, 12 September 2008

If we consider the squaring rule


\displaystyle \left( x-a \right)^{2}=x^{2}-2ax+a^{2}

and move \displaystyle a^{2} over to the left-hand side, we obtain the formula


\displaystyle \left( x-a \right)^{2}-a^{2}=x^{2}-2ax


\displaystyle


With the help of this formula, we can rewrite (complete the square of) a mixed expression \displaystyle x^{2}-2ax to a obtain a quadratic expression, \displaystyle \left( x-a \right)^{2}-a^{2} .

The expression \displaystyle x^{2}-2x corresponds to \displaystyle a=1 in the formula above and thus


\displaystyle x^{2}-2x=\left( x-1 \right)^{2}-1

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