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CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 282
Resolver las ecuaciones:
  1. x 4 1 =0 ( x 2 +1 ) ( x 2 1 ) =0 ( x 2 +1 ) (x+1 ) (x1 ) =0 x 1 +1 =0 x 1 =1 x 2 1 =0 x 2 =1 x 2 +1 =0 x 2 =1 x = ± 1 x 3 =i x 4 =i
  2. x 3 +1 =0 (x+1 ) ( x 2 x+1 ) =0 x+1 =0 x 1 =1 x 2 x+1 =0 x = (1 ) ± (1 ) 2 4( 1 ) ( 1 ) 2( 1 ) x = 1 ± 14 2 x = 1 ± 1 3 2 x = 1 ± 3 i 2 x 1 = 1+ 3 i 2 x 2 = 1 3 i 2
  3. x 4 =81 x 4 81 =0 ( x 2 +9 ) ( x 2 9 ) =0 ( x 2 +9 ) (x3 ) (x+3 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +9 =0 x 2 =9 x = ± 3 2 x = ± 3 1 x 3 =3i x 4 =3i
  4. x 4 256 =0 ( x 2 +16 ) ( x 2 16 ) =0 ( x 2 +16 ) (x4 ) (x+4 ) =0 x 1 4 =0 x 1 =4 x 2 +4 =0 x 2 =4 x 2 +16 =0 x 2 =16 x = ± 4 2 x = ± 4 1 x 3 =4i x 4 =4i
  5. x 3 +8 =0 (x+2 ) ( x 2 2x+4 ) =0 x 1 +2 =0 x 1 =2 x 2 2x+4 =0 x = (2 ) ± (2 ) 2 4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 416 2 x = 2 ± 12 2 x = 2 ± (3 ) ( 2 2 ) 2 x = 2 ± 2 ( 3 ) (1 ) 2 x = 2 (1 ± 3 i ) 2 x 2 =1+ 3 i x 3 =1 3 i
  6. x 4 625 =0 ( x 2 +25 ) ( x 2 25 ) =0 ( x 2 +25 ) (x5 ) (x+5 ) =0 x 1 5 =0 x 1 =5 x 2 +5 =0 x 2 =5 x 2 +25 =0 x 2 =25 x = ± 25 x = ± (1 ) ( 5 2 ) x = ± 5i x 3 =5i x 4 =5i
  7. x 3 +64 =0 (x+4 ) ( x 2 4x+16 ) =0 x+4 =0 x 1 +4 =0 x 1 =4 x 2 4x+16 =0 x = (4 ) ± (4 ) 2 4( 1 ) ( 16 ) 2( 1 ) x = 4 ± 1664 2 x = 4 ± 48 2 x = 4 ± (3 ) ( 4 2 ) 2 x = 4 ± 4 3 1 2 x = 2 (2 ± 2 3 i ) 2 x 2 =2+2 3 i x 3 =22 3 i
  8. x 6 729 =0 ( x 3 27 ) ( x 3 +27 ) =0 (x3 ) ( x 2 +3x+9 ) (x+3 ) ( x 2 3x+9 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +3x+9 =0 x = 3 ± 3 2 4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 936 2 x = 3 ± 27 2 x = 3 ± (1 ) ( 3 3 ) 2 x = 3 ± 3 3 1 2 x = 3 ± 3 3 i 2 x 3 = 33 3 i 2 x 4 = 3+3 3 i 2 x 2 3x+9 =0 x = (3 ) ± (3 ) 2 4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 936 2 x = 3 ± 27 2 x = 3 ± (1 ) ( 3 3 ) 2 x = 3 ± 3 3 1 2 x = 3 ± 3 3 i 2 x 5 = 33 3 i 2 x 6 = 3+3 3 i 2
  9. Hallar las raíces cúbicas de 8.
    x 3 =8 x 3 8 =0 (x2 ) ( x 2 +2x+4 ) =0 x 1 2 =0 x 1 =2 x 2 +2x+4 =0 x = 2 ± 2 2 4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 416 2 x = 2 ± 12 2 x = 2 ± (1 ) ( 3 ) ( 2 2 ) 2 x = 2 ± 2 1 3 2 x = 2 (1 ± 3 i ) 2 x 2 =1+ 3 i x 3 =1 3 i
  10. Hallar las raíces cuartas de 64.
    x 4 =64 x 4 64 =0 ( x 2 +8 ) ( x 2 8 ) =0 x 2 8 =0 x 2 =8 x = ± 8 x = ± 2 3 x = ± 2 2 x 1 =2 2 x 2 =2 2 x 2 +8 =0 x 2 =8 x = ± 8 x = ± 2 3 x = ± 2 2 1 x 1 =2 2 i x 2 =2 2 i