Konjugatregeln
Konjugatregeln
Så här ser den ut: a2-b2 = (a-b)(a+b) utför multiplikationen: (a - b)(a + b) = a2 + ab - ba - b2 vi kan stryka ab - ba = ab - ab = 0: (a - b)(a + b) = a2 - b2 V.S.B.
Konjugatregeln med <math> [math]\displaystyle{ \LaTeX }[/math] </math>
Så här ser beviset ut med LaTeX: [math]\displaystyle{ (a-b)\cdot(a+b) }[/math] [math]\displaystyle{ = a^2 +a\cdot b -a\cdot b -b^2 }[/math] [math]\displaystyle{ = a^2-b^2 }[/math] [math]\displaystyle{ \blacksquare }[/math]
Tips för dem som upprätthåller Wikisidorna ( skriv såhär i Wikitexten och googla typsättning med TeX för råd ): <math>(a-b)\cdot(a+b)</math> <math> = a^2 +a\cdot b -a\cdot b -b^2 </math> <math> = a^2-b^2 </math> <math> \blacksquare </math>
Film
Bondestam (tv) respektive Matteboken (th) förklarar:
Geometriskt bevis av konjugatregeln
Första beviset
Andra beviset
Visualisering
Här gäller: [math]\displaystyle{ (x-y)\cdot(x+y) = x^2 - y^2 }[/math] Denna är gjord med Geogebra, sparad som animerad gif, upladdad till WIKIMEDIA COMMONS och länkad hit. [math]\displaystyle{ (a - b)\cdot(a + b) = a^2 - b^2 }[/math]
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Uppgifter
Övningar (utan räknare)
1. [math]\displaystyle{ 1992\cdot 2008 = ? }[/math] 2. Lös [math]\displaystyle{ x^2-1=0 }[/math] för alla reella x.
Tips : Använd konjugatregeln och nollregeln för ekvationen.
Webbmatte