Wiskunde week 2, antw - Opgavencollege Wiskunde 1, 17...

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Unformatted text preview: Opgavencollege Wiskunde 1, 17 September 2010 Les 2 Uitwerkingen Opgavencollege Wiskunde 1 Les 2 Uitwerkingen Pag. 1/4 • Opgave 1 a) ( 29 2 2 8 16 4 4 + + = ⇔ + = ⇔ = - x x x x b) ( 29 2 2 10 25 5 5- + = ⇔- = ⇔ = x x x x c) ( 29 ( 29 2 72 9 8 8 9 x x x x x x-- = ⇔- + = ⇔ = - ∨ = d) ( 29 ( 29 2 7 18 9 2 9 of 2 +- = ⇔ +- = ⇔ = - = x x x x x x e) 6 6 6 1 1 1 1 64 64 2 64- = ⇔ = ⇔ = ± = ± x x x f) 3 3 3 3 3 1 1 1 1 125 5 5 5- = ⇔ = ⇔ = = x x x g) 2 ( 1) 16 ( 1) 4 1 4 3 5 x x x x x- = ⇔- = ± ⇔ = ± ⇔ = - ∨ = Opmerking: De vergelijking is te schrijven als: 2 2 2 1 16 2 15 5 3 5 of 3 ( )( ) x x x x x x x x- + = ⇔-- = ⇔- + = ⇔ = = - Dit is natuurlijk niet de meest efficiënte manier van oplossen (maar wel goed). h) 4 4 ( 1) 16 1 16 2 1 3 x x x x- = ⇔- = ± = ± ⇔ = - ∨ = i) 2 2 2 2 4 6 4 2 4 2 2 1 x x x x x x-- + = ⇔ -- + = ⇔ +- = ⇔ 2 4 4 1 ( 1) 1 2 1 2 2 1 x x x- ±- ⋅ ⋅ - = ⇔ = - - ∨ = - + ⋅ j) 2 2 3 3 9 4 1 5 3 3 3 3 3 2 2 5 1 3 of 2 2 2 1 2 2 x x x x x x x x- ±- ⋅ ⋅- +- -- +- =- ⇔ + + = ⇔ = ⇔ = = ⋅ • Opgave 2 Algemene opmerking: Wanneer ( 29 2 f x ax bx c = + + twee nulpunten ( 29 1 ,0 x en ( 29 2 ,0 x heeft , valt ( 29 f x te ontbinden in ( 29 ( 29 1 2 a x x x x-- . a) ( 29 ( 29 2 6 4 3 13 3 13 x x x x +- = +- + + 6 36 4 1 4 6 2 13 [ : 3 13] 2 1 2 abc formule x x- ±- ⋅ ⋅ -- ±- = = → = - ± ⋅ b) ( 29 ( 29 ( 29 2 2 2 8 8 2 4 4 2 2 2 2 2 2 2 4 16 4 1 4 4 32 [ : 2 2 2] 2 1 2 x x x x x x abc formule x x-- + = - +- = - +- +...
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Wiskunde week 2, antw - Opgavencollege Wiskunde 1, 17...

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