2 Lineare Gleichungssysteme - Duden Paetec

Quadratische Gleichungen und Gleichungen höheren Grades 499. a) L = 8; – 8 b) L = 1; – 1 c) L = 0 d) L = 0,4; – 0,4 e) L = 1-- ; – 1--7 7f) L = 3-- ; – 3-- g) L = ∅ h) L = 7-- ; – 7--i) L = ∅ j) L = ∅2 2 5 510. a) x 1 = 5 ; x 2 = – 5 b) x 1 = 10 ; x 2 = – 10 c) x 1 = 20 ; x 2 = – 20d) x 1 = --------- 19 ; x 2 = – --------- 19 e) x 1 = ------ 3 ; x 2 = – ------ 32 2 2 211. a) x 1 = 2,83; x 2 = – 2,83 b) x 1 = 2,12; x 2 = – 2,12 c) x 1 = 3,87; x 2 = – 3,87d) keine Lösung e) x 1 = 1,53; x 2 = – 1,5312. a) x 1 = 5; x 2 = – 1 b) x 1 = – 1; x 2 = – 13 c) x 1 = 2; x 2 = 0d) x 1 = 2; x 2 = – 1 e) keine Lösung13. a) L = 1; – 3 b) L = 10; 8 c) L = 6 d) L = 5; 15e) L = 2,2; – 1,2 f) L = 4; 0 g) L = 6; 0 h) L = 1,5; – 6,514. a) x 1 = 9; x 2 = – 9 b) x 1 = 4,5; x 2 = – 4,5 c) x 1 = 1-- ; x 2 = – 1--4 4e) L = { 3-- ; – 3--} f) x 1 = 2; x 2 = – 27 7d) x 1 = 3; x 2 = – 315. a) (x – 1)(x + 1) = 0 b) (x – 4)(x + 4) = 0 c) (3x – 5)(3x + 5) = 0 d) L = ∅x 1 = 1; x 2 = – 1 x 1 = 4; x 2 = – 4 x 1 = 5-- ; x 2 = – 5--3 316. a) x 1 = 3; x 2 = – 3 b) x 1 = 4; x 2 = – 4 c) x 1 = 6; x 2 = – 6 d) x 1 = 6; x 2 = – 6e) x 1 = 12; x 2 = – 12 f) L = ∅ g) x 1 = 12 ; x 2 = – 12 h) x 1 = x 2 = 0i) x 1 = 2 ; x 2 = – 2 j) x 1 = 2; x 2 = – 2 k) L = ∅ l) x 1 = 4; x 2 = – 417. a) n = 17 b) z 1 = 19; z 2 = – 19c)x 1 = 4; x 2 = – 4d)x 1 =13; x 2 = – 13e) n = 24 f) x 1 = 9; x 2 = – 918. a) A O = 6a 2 = 121,5 cm 2 ⇒ a = 4,5 cm b) V = a 3 = 91,125 cm 319. A = a ⋅ b = a ⋅ 2a = 2a 2 = 512 cm 2 ⇒ a = 16 cm; b = 32 cm ⇒ u = 96 cmSeite 10620. 20,5 m 21. A = 1-- ab = 1-- a ⋅ 3-- a = 3--a 2 = 147 cm 2 ⇒ a = 14 cm; b = 21 cm2 2 2 422. A = 2535 cm2 = l ⋅ b -- l = 5--l = 65 cm b = 39 cmb 3Lösen spezieller Gleichungen durch inhaltliche Überlegungen23. a) x 1 = 0; x 2 = 3 b) x 1 = 7; x 2 = 0 c) x 1 = 0; x 2 = – 11 d) x 1 = 0; x 2 = 2 e) x 1 = 0; x 2 = –324. a) x(x – 14) = 0 ⇒ x 1 = 0; x 2 = 14 b) x(x + 6) = 0 ⇒ x 1 = 0; x 2 = – 6 c) x(x – 1-- ) = 0 ⇒ x 1 = 0; x 2 = 1--22d) x(x – 1) = 0 ⇒ x 1 = 0; x 2 = 1 e) x(– x + 2) = 0 ⇒ x 1 = 0; x 2 = 225. a) L = 0; – 1 b) L = 0; 2 c) L = 0; 6 d) L = 0; 1,6e) L = 0; – 1,5 f) L = 0; 1--g) L = 0; – 1226. a) ja b) nein; 1 ist keine Lösung. c) nein; – 8 ist keine Lösung.d) nein; 8 ist keine Lösung. e) ja