Ejercicio 283

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CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 283
Resolver las ecuaciones siguientes, hallando todas las raíces:
  1. x 4 10 x 2 +9 =0 ( x 2 9 ) ( x 2 1 ) =0 (x3 ) (x+3 ) (x1 ) (x+1 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 3 1 =0 x 3 =1 x 4 +1 =0 x 4 =1
  2. x 4 13 x 2 +36 =0 ( x 2 4 ) ( x 2 9 ) =0 (x2 ) (x+2 ) (x3 ) (x+3 ) =0 x 1 2 =0 x 1 =2 x 2 +2 =0 x 2 =2 x 3 3 =0 x 3 =3 x 4 +3 =0 x 4 =3
  3. x 4 29 x 2 +100 =0 ( x 2 25 ) ( x 2 4 ) =0 (x5 ) (x+5 ) (x2 ) (x+2 ) =0 x 1 5 =0 x 1 =5 x 2 +5 =0 x 2 =5 x 3 2 =0 x 3 =2 x 4 +2 =0 x 4 =2
  4. x 4 61 x 2 +900 =0 ( x 2 36 ) ( x 2 25 ) =0 (x6 ) (x+6 ) (x5 ) (x+5 ) =0 x 1 6 =0 x 1 =6 x 2 +6 =0 x 2 =6 x 3 5 =0 x 3 =5 x 4 +5 =0 x 4 =5
  5. x 4 +3 x 2 4 =0 ( x 2 +4 ) ( x 2 1 ) =0 ( x 2 +4 ) (x1 ) (x+1 ) =0 x 1 1 =0 x 1 =1 x 2 +1 =0 x 2 =1 x 2 +4 =0 x 2 =4 x = ± (1 ) ( 2 ) 2 x = ± 2 1 x = ± 2i x 3 =2i x 4 =2i
  6. x 4 +16 x 2 225 =0 ( x 2 +25 ) ( x 2 9 ) =0 ( x 2 +25 ) (x3 ) (x+3 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +25 =0 x 2 =25 x = ± (1 ) ( 5 2 ) x = ± 5 1 x = ± 5i x 3 =5i x 4 =5i
  7. x 4 45 x 2 196 =0 ( x 2 49 ) ( x 2 +4 ) =0 (x7 ) (x+7 ) ( x 2 +4 ) =0 x 1 7 =0 x 1 =7 x 2 +7 =0 x 2 =7 x 2 +4 =0 x 2 =4 x = ± 2 2 x = ± 2 1 x = ± 2i x 3 =2i x 4 =2i
  8. x 4 6 x 2 +5 =0 ( x 2 5 ) ( x 2 1 ) =0 ( x 2 5 ) (x1 ) (x+1 ) =0 x 1 1 =0 x 1 =1 x 2 +1 =0 x 2 =1 x 2 5 =0 x = ± 5 x 3 = 5 x 4 = 5
  9. 4 x 4 37 x 2 +9 =0 4 x 4 x 2 36 x 2 +9 =0 x 2 (4 x 2 1 ) 9(4 x 2 1 ) =0 ( x 2 9 ) (4 x 2 1 ) =0 (x3 ) (x+3 ) (4 x 2 1 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 4 x 2 1 =0 4 x 2 =1 x 2 = 1 4 x = ± 1 4 x = ± 1 2 1 x 3 = 1 2 1 x 4 = 1 2 1
  10. 9 x 4 40 x 2 +16 =0 9 x 4 36 x 2 4 x 2 +16 =0 9 x 2 ( x 2 4 ) 4( x 2 4 ) =0 (9 x 2 4 ) ( x 2 4 ) =0 (9 x 2 4 ) (x2 ) (x+2 ) =0 x 1 2 =0 x 1 =2 x 2 +2 =0 x 2 =2 9 x 2 4 =0 9 x 2 =4 x 2 = 4 9 x = ± 4 9 x = ± 2 3 x 3 = 2 3 x 4 = 2 3
  11. 25 x 4 +9 x 2 16 =0 25 x 4 +25 x 2 16 x 2 16 =0 25 x 2 ( x 2 +1 ) 16( x 2 +1 ) =0 (25 x 2 16 ) ( x 2 +1 ) =0 x 2 +1 =0 x 2 =1 x = ± 1 x 1 =i x 2 =i 25 x 2 16 =0 25 x 2 =16 x 2 = 16 25 x = ± 16 25 x = ± 4 5 x 3 = 4 5 x 4 = 4 5
  12. 4 x 4 +11 x 2 3 =0 4 x 4 x 2 +12 x 2 3 =0 x 2 (4 x 2 1 ) +3(4 x 2 1 ) =0 ( x 2 +3 ) (4 x 2 1 ) =0 4 x 2 1 =0 4 x 2 =1 x 2 = 1 4 x = ± 1 4 x = ± 1 2 x 1 = 1 2 x 2 = 1 2 x 2 +3 =0 x 2 =3 x = ± 3 x = ± 1 3 x = ± 3 i x 3 = 3 i x 4 = 3 i
  13. (2 x 2 +1 ) 2 ( x 2 3 ) 2 =80 [(2 x 2 +1 ) ( x 2 3 ) ] [(2 x 2 +1 ) +( x 2 3 ) ] =80 [2 x 2 +1 x 2 +3 ] [2 x 2 +1+ x 2 3 ] =80 ( x 2 +4 ) (3 x 2 2 ) =80 3 x 4 2 x 2 +12 x 2 8 =80 3 x 4 +10 x 2 88 =0 3 x 4 12 x 2 +22 x 2 88 =0 3 x 2 ( x 2 4 ) +22( x 2 4 ) =0 (3 x 2 +22 ) ( x 2 4 ) =0 x 2 4 =0 x = ± 4 x = ± 2 x 1 =2 x 2 =2 3 x 2 +22 =0 3 x 2 =22 x 2 = 22 3 x = ± 22 3 x = ± (1 ) ( 22 3 ) x = ± 22 3 i x 3 = 22 3 i x 4 = 22 3 i
  14. x 2 (3 x 2 +2 ) =4( x 2 3 ) +13 3 x 4 +2 x 2 =4 x 2 12+13 3 x 4 +2 x 2 4 x 2 1 =0 3 x 4 2 x 2 1 =0 3 x 4 3 x 2 + x 2 1 =0 3 x 2 ( x 2 1 ) +( x 2 1 ) =0 (3 x 2 +1 ) ( x 2 1 ) =0 x 2 1 =0 x 2 =1 x = ± 1 x = ± 1 x 1 =1 x 2 =1 3 x 2 +1 =0 3 x 2 =1 x 2 = 1 3 x = ± 1 3 x = ± (1 ) ( 1 3 ) x = ± 1 3 i x 3 = 1 3 i x 4 = 1 3 i