Ejercicio 267

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CAPITULO XXXIII

Ecuaciones de segundo grado
Ejercicio 267
Resolver las siguientes ecuaciones aplicando la fórmula particular:
x= m 2 ± m 2 4 n
  1. x 2 3x+2 =0 m=3 n=2 x= 3 2 ± (3 ) 2 4 2 x= 3 2 ± 9 4 2 x= 3 2 ± 98 4 x= 3 2 ± 1 4 x= 3 2 ± 1 2 x 1 = 3 2 + 1 2 = 2 x 1 =2 x 2 = 3 2 1 2 = 2 2 x 2 =1
  2. x 2 2x15 =0 m=2 n=15 x= 2 2 ± (2 ) 2 4 (15 ) x=1 ± 4 4 +15 x=1 ± 1+15 x=1 ± 16 x=1 ± 4 x 1 =1+4 x 1 =5 x 2 =14 x 2 =3
  3. x 2 =19x88 x 2 19x+88 =0 m=19 n=88 x= 19 2 ± (19 ) 2 4 88 x= 19 2 ± 361 4 88 x= 19 2 ± 361352 4 x= 19 2 ± 9 4 x= 19 2 ± 3 2 x 1 = 19 2 + 3 2 = 2 x 1 =11 x 2 = 19 2 3 2 = 2 x 2 =8
  4. x 2 +4x =285 x 2 +4x285 =0 m=4 n=285 x= 2 ± 4 2 4 (285 ) x=2 ± 4+285 x=2 ± 289 x=2 ± 17 x 1 =2+17 x 1 =15 x 2 =217 x 2 =19
  5. 5x(x1 ) 2(2 x 2 7x ) =8 5 x 2 5x4 x 2 +14x+8 =0 x 2 +9x+8 =0 m=9 n=8 x= 9 2 ± 9 2 4 8 x= 9 2 ± 81 4 8 x= 9 2 ± 8132 4 x= 9 2 ± 49 4 x= 9 2 ± 7 2 x 1 = 9 2 + 7 2 = 9+7 2 = 2 2 x 1 =1 x 2 = 9 2 7 2 = 97 2 = 2 x 2 =8
  6. x 2 (7x+6 ) =x+59 x 2 7x6x59 =0 x 2 8x65 =0 m=8 n=65 x= 2 ± 8 2 4 (65 ) x=4 ± 4 +65 x=4 ± 16+65 x=4 ± 81 x=4 ± 9 x 1 =4+9 x 1 =13 x 2 =49 x 2 =5
  7. (x1 ) 2 +11x+199 =3 x 2 (x2 ) 2 x 2 2x+1+11x+199 =3 x 2 ( x 2 4x+4 ) x 2 +9x+200 =3 x 2 x 2 +4x4 x 2 +9x+2002 x 2 4x+4 =0 x 2 +5x+204 =0 x 2 5x204 =0 m=5 n=204 x= 5 2 ± (5 ) 2 4 (204 ) x= 5 2 ± 25 4 +204 x= 5 2 ± 25+816 4 x= 5 2 ± 841 4 x= 5 2 ± 29 2 x 1 = 5 2 + 29 2 = 5+29 2 = 2 x 1 =17 x 2 = 5 2 29 2 = 529 2 = 2 x 2 =12
  8. (x2 ) (x+2 ) 7(x1 ) =21 x 2 47x+7 =21 x 2 7x+321 =0 x 2 7x18 =0 m=7 n=17 x= 7 2 ± (7 ) 2 4 (18 ) x= 7 2 ± 49 4 +18 x= 7 2 ± 49+72 4 x= 7 2 ± 121 4 x= 7 2 ± 11 2 x 1 = 7 2 + 11 2 = 7+11 2 = 2 x 1 =9 x 2 = 7 2 11 2 = 711 2 = 2 x 2 =2
  9. 2 x 2 (x2 ) (x+5 ) =7(x+3 ) 2 x 2 ( x 2 +3x10 ) =7x+21 2 x 2 x 2 3x+107x21 =0 x 2 10x11 =0 m=10 n=11 x= 2 ± (10 ) 2 4 (11 ) x=5 ± 4 +11 x=5 ± 25+11 x=5 ± 36 x=5 ± 6 x 1 =5+6 x 1 =11 x 2 =56 x 2 =1
  10. (x1 ) (x+2 ) (2x3 ) (x+4 ) x+14 =0 x 2 + x 2(2 x 2 +8x3x12 ) x +14 =0 x 2 2 x 2 5x+12+12 =0 x 2 5x+24 =0 x 2 +5x24 =0 m=5 n=24 x= 5 2 ± 5 2 4 (24 ) x= 5 2 ± 25 4 +24 x= 5 2 ± 25+96 4 x= 5 2 ± 121 4 x= 5 2 ± 11 2 x 1 = 5 2 + 11 2 = 5+11 2 = 2 x 1 =3 x 2 = 5 2 11 2 = 511 2 = 2 x 2 =8