Ejercicio 284

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CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 284
Resolver las ecuaciones:
  1. x 6 7 x 3 8 =0 x 6 8 x 3 + x 3 8 =0 x 3 ( x 3 8 ) +( x 3 8 ) =0 ( x 3 8 ) ( x 3 +1 ) =0 (x2 ) ( x 2 +2x+4 ) (x+1 ) ( x 2 x+1 ) =0 x 1 2 =0 x 1 =2 x 2 +1 =0 x 2 =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 3 =1+ 3 i x 4 =1 3 i 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 5 = 1+ 3 i 2 x 6 = 1 3 i 2
  2. x 6 +30 x 3 +81 =0 x 6 +27 x 3 +3 x 3 +81 =0 x 3 ( x 3 +27 ) +3( x 3 +27 ) =0 ( x 3 +3 ) ( x 3 +27 ) =0 ( x 3 +3 ) (x+3 ) ( x 2 3x+9 ) =0 x 1 3 +3 =0 x 1 3 =3 x 1 = 3 3 x 1 = 33 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
  3. 8 x 6 +15 x 3 2 =0 8 x 6 +16 x 3 x 3 2 =0 8 x 3 ( x 2 +2 ) ( x 3 +2 ) =0 (8 x 3 1 ) ( x 3 +2 ) =0 8 x 1 3 1 =0 8 x 1 3 =1 x 1 3 = 1 8 x 1 = 1 8 x 1 = 1 2 x 2 3 +2 =0 x 2 3 =2 x 2 = 2 3 x 2 = 23
  4. x 8 41 x 4 +400 =0 x 8 16 x 4 25 x 4 +400 =0 x 4 ( x 4 16 ) 25( x 4 16 ) =0 ( x 4 25 ) ( x 4 16 ) =0 ( x 2 +5 ) ( x 2 5 ) ( x 2 4 ) ( x 2 +4 ) =0 ( x 2 +5 ) ( x 2 5 ) ( x 2 +4 ) (x+2 ) (x2 ) =0 x 1 +2 =0 x 1 =2 x 2 2 =0 x 2 =2 x 2 +5 =0 x 2 =5 x = ± 5 x 3 = 5 i x 4 = 5 i x 2 5 =0 x 2 =5 x = ± 5 x 5 = 5 x 6 = 5 x 2 +4 =0 x 2 =4 x = ± 4 x = ± (1 ) ( 2 2 ) x = ± 2 1 x = ± 2i x 7 =2i x 8 =2i
  5. x 10 33 x 5 +32 =0 x 10 x 5 32 x 5 +32 =0 x 5 ( x 2 1 ) 32( x 5 1 ) =0 ( x 5 32 ) ( x 5 1 ) =0 x 5 32 =0 x 5 =32 x 1 = 325 x 1 =2 x 5 1 =0 x 5 =1 x = 15 x 2 =1
  6. x 4 13 x 2 +36 =0 ( x 2 9 ) ( x 2 4 ) =0 x 2 9 =0 x 2 =9 1 x 2 =9 x 2 = 1 9 x = ± 1 9 x = ± 1 3 x 1 = 1 3 x 2 = 1 3 x 2 4 =0 x 2 =4 1 x 2 =4 x 2 = 1 4 x = ± 1 4 x = ± 1 2 x 3 = 1 2 x 4 = 1 2
  7. x 6 +35 x 3 =216 x 6 +35 x 3 +216 =0 x 6 +27 x 3 +8 x 3 +216 =0 x 3 ( x 3 +27 ) +8( x 3 +27 ) =0 ( x 3 +8 ) ( x 3 +27 ) =0 x 3 +8 =0 x 3 =8 1 x 3 =8 x 3 = 1 8 x 1 = 1 8 3 x 1 = 1 2 x 3 +27 =0 x 3 =27 1 x 3 =27 x 3 = 1 27 x 2 = 1 27 3 x 2 = 1 3
  8. x 10 =242 x 5 +243 x 10 242 x 5 243 =0 ( x 5 243 ) ( x 5 +1 ) =0 x 5 243 =0 x 5 =243 1 x 5 =243 x 5 = 1 243 x 1 = 1 243 5 x 1 = 1 3 x 5 +1 =0 x 5 =1 1 x 5 =1 x 5 =1 x 2 = 1 5 x 2 =1
  9. x 3 9 x 3 2 +8 =0 x 3 x 3 2 8 x 3 2 +8 =0 x 3 2 ( x 3 2 1 ) 8( x 3 2 1 ) =0 ( x 3 2 8 ) ( x 3 2 1 ) =0 x 3 2 8 =0 x 3 2 =8 ( x 3 2 ) 2 3 = 8 2 3 x 1 = 8 2 3 x 1 = 643 x 1 =4 x 3 2 1 =0 ( x 3 2 ) 2 3 = 1 2 3 x 2 =1
  10. x+ x 1 2 =6 x2 x 1 2 +3 x 1 2 6 =0 x 1 2 ( x 1 2 2 ) +3( x 1 2 2 ) =0 ( x 1 2 +3 ) ( x 1 2 2 ) =0 x 1 2 +3 =0 x 1 2 =3 ( x 1 2 ) 2 = (3 ) 2 x 1 =9 x 1 2 2 =0 x 1 2 =2 ( x 1 2 ) 2 = 2 2 x 2 =4
  11. 3x =16 x 5 3x16 x 1 2 +5 =0 3x x 1 2 15 x 1 2 +5 =0 x 1 2 (3 x 1 2 1 ) 5(3 x 1 2 1 ) =0 ( x 1 2 5 ) (3 x 1 2 1 ) =0 x 1 2 5 =0 x 1 2 =5 ( x 1 2 ) 2 = 5 2 x 1 =25 3 x 1 2 1 =0 3 x 1 2 =1 x 1 2 = 1 3 ( x 1 2 ) 2 = ( 1 3 ) 2 x = 1 9
  12. 2 x 1 2 5 x 1 4 +2 =0 2 x 1 2 x 1 4 4 x 1 4 +2 =0 x 1 4 (2 x 1 4 1 ) 2(2 x 1 4 1 ) =0 ( x 1 4 2 ) (2 x 1 4 1 ) =0 x 1 4 2 =0 x 1 4 =2 ( x 1 4 ) 4 = 2 4 x 1 =16 2 x 1 4 1 =0 2 x 1 4 =1 x 1 4 = 1 2 ( x 1 4 ) 4 = ( 1 2 ) 4 x 2 = 1 16