From Förberedande kurs i matematik 1

Revision as of 10:03, 1 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_3d.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (08:39, 29 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	Because both terms, <math>x(x+3)</math> and <math>x(2x-9)</math>, contain the factor <math>x</math>, we can take out <math>x</math> from the left-hand side and collect together the remaining expression,
-	<center> [[Bild:2_3_3d.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\begin{align}
		+	x(x+3)-x(2x-9)
		+	&= x\bigl((x+3)-(2x-9)\bigr)\\[5pt]
		+	&= x(x+3-2x+9)\\[5pt]
		+	&= x(-x+12)\,\textrm{.}
		+	\end{align}</math>}}
		+
		+	The equation is thus
		+
		+	{{Displayed math||<math>x(-x+12) = 0</math>}}
		+
		+	and we obtain directly that the equation is satisfied if either <math>x</math> or <math>-x+12</math> is zero. The solutions to the equation are therefore <math>x=0</math> and <math>x=12</math>.
		+
		+	Here, it can be worth checking that <math>x=12</math> is a solution (the case
		+	<math>x=0</math> is obvious)
		+
		+	{{Displayed math||<math>\text{LHS} = 12\cdot (12+3) - 12\cdot (2\cdot 12-9) = 2\cdot 15 - 12\cdot 15 = 0 = \text{RHS.}</math>}}

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Current revision

Because both terms, \displaystyle x(x+3) and \displaystyle x(2x-9), contain the factor \displaystyle x, we can take out \displaystyle x from the left-hand side and collect together the remaining expression,

\displaystyle \begin{align} x(x+3)-x(2x-9) &= x\bigl((x+3)-(2x-9)\bigr)\\[5pt] &= x(x+3-2x+9)\\[5pt] &= x(-x+12)\,\textrm{.} \end{align}

The equation is thus

\displaystyle x(-x+12) = 0

and we obtain directly that the equation is satisfied if either \displaystyle x or \displaystyle -x+12 is zero. The solutions to the equation are therefore \displaystyle x=0 and \displaystyle x=12.

Here, it can be worth checking that \displaystyle x=12 is a solution (the case \displaystyle x=0 is obvious)

\displaystyle \text{LHS} = 12\cdot (12+3) - 12\cdot (2\cdot 12-9) = 2\cdot 15 - 12\cdot 15 = 0 = \text{RHS.}